Free videos to help you learn and understand concepts in Calculus.

I take the derivative of a complex fraction using Logarithmic Differentiation and Implicit Differentiation.  This difficult example would be much more work if your only tools were the Product Rule and Quotient Rule.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by chapters within each subject.

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OVERSEAS

Logarithmic Differentiation Derivative of a Fraction

EXAMPLE: Solving an equation using logarithms 6:24
EXAMPLE: Sketching a natural exponential equation with transformations 8:05
EXAMPLES: Derivatives of natural exponential functions 14:26 17:38 22:24
                    ... involving Second Fundamental Theorem of Calculus 24:34
                    ....involving Implicit Differentiation 27:10

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Derivative of Natural Exponential Function e^x Calculus 1 AB

EXAMPLES AT 4:06 8:24 10:18 15:09 25:10 31:17
At 24:20 I have a copy error.  I meant to write 1^2-u^2 and not 1^2+u^2
The last line of the last example should be 1/2*cos^-1(2/15) - 1/2*cos^-1(2/5).  There is an annotation correction.

Integration with an Inverse Trigonometric Function in the Integrand
   • Integrating Inverse Trigonometric Fun...   Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Integration Involving Inverse Trigonometric Functions Calculus 1 AB 6 Examples

I introduce the concept of finding the general Antiderivative through the process of Indefinite Integration.  I finish by working through many examples. NOTE: I miscopied the Power Rule writing that n can't equal 1, there is an annotation correction, n cannot equal -1.

NOTE: At min 9:00 I verbal say the derivative of 3x is 3x^2 which is incorrect.  It is 3.  You will not see the annotation correction if viewing on an iPad or iPhone.
Please help Close Caption this lesson
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Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Antiderivative & Indefinite Integration 11 Examples Calculus 1 AB

EXAMPLES at 3:09 9:01 10:37 11:36
I work through finding Definite Integrals when the upper boundary, and possibly the lower bound of the closed interval is a variable expression instead of a constant.  Four examples are completed. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Definite Integral as a Function of X Calculus 1 AB

EXAMPLES Rational Functions 7:57 14:45 17:25 Irrational Functions 24:25 33:02 39:15 Trig Functions 47:01 47:40
As I lectured I misspoke a few times, at about 2:29 I should have said vertical distance, 8:20 we are looking for the highest degree of the denominator, and at 23:07 x greater than n like it was written.
In the third example at 17:25, you should divide by the largest degree in the denominator, so I should be dividing by x^3 or multiplying by 1/x^3 here.  Luckily my final answer is still correct.  I would have had 0/1=0.  I incorrectly say in this lesson that the square root of x squared is x.  The square root of x squared is the absolute value of x.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Limits at Infinity Rational, Irrational, and Trig Functions Calculus 1 AB READ DESCRIPTION

I show you how to estimate the area bound by a function and the x-axis on a closed interval [a,b] using rectangles.  Depending on whether you inscribe or circumscribe your rectangles you will find the upper sum (over estimate the area) or the lower sum (underestimate the area).  The more rectangles used the better your estimate.  This video is the first part of my full length video "Area of a Plane w/Rectangles Limit of Infinite Sum"

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Estimating Area with Rectangles Part 1 of 2 Calculus 1 AB

I work through an example of how to use the first and second derivative in an application problem. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Higher Order Derivative Introduction Calculus 1 AB

I work through three examples of finding derivatives of Inverse Trigonometric Functions at 1:20 3:57 7:24 Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Derivative of Inverse Trigonometric Functions Examples Calculus 1 AB

If given an Initial Condition (which is a given point a graph passes through) we are able to find a Particular Solution.  In other words, instead of just finding a general antiderivative we will be able to find the antiderivative given a derivative and a point the original function passes through Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Initial Condition Particular Solution for Antiderivative Calculus 1 AB

I introduce how to integrate exponential functions with base a.  I derive the integration rule and then work through 4 examples.  Derivation at 3:46  EXAMPLES at 9:25 15:00 17:57 24:50 Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Integrating Exponential Functions Base a Calculus 1 AB

5 Examples of sketching derivative functions from a graph starting at 1:27 6:27 11:13 16:40 and graphing an antiderivative from a derivative at 20:19

Original Lesson Graphical Comparison of Functions vs Derivative Graphs,    • Graphical Comparison of Function vs D...  

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Sketching Derivatives from Graphs of Functions 5 Examples Calculus 1 AB

I introduce estimating the Area in a Plane using rectangles.  I then expand on that concept using summation notation and limits at n approached infinity to find the exact area bound by a function and the x-axis within a closed interval.  This video includes examples of estimating the lower and upper sums with rectangles and finding exact area with infinite sums.  

When I wrote the formula for the Upper Sum, the upper bound of the sigma notation should be n, not Infiniti. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Estimating Area with Rectangles & Riemann Limit of Sums Definition of Area Calculus 1 AB

EXAMPLES at 10:26 13:51 16:16 26:33 29:55 NOTE:At minute 29:16 I say the denominator equals zero, but it is undefined at pi/2.
I introduce and explain the Infinite Limits Theorem and the Definition of Vertical Asymptotes and then work through five examples.  The first three examples involve algebraic rational functions and I remind you of the difference of asymptotes and holes (removable discontinuities) and the last two involve Trig functions in the rational equations.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class.  

You can also find me at:

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Infinite Limits & Vertical Asymptotes Calculus 1 AB

I extend my lesson of Derivative of Natural Logarithms to Logs of any Base a.  EXAMPLES at 4:29 7:29 8:33 Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Derivative of Logarithms Base a Calculus 1 AB

I introduce the Definition of Area of a Plane.  This is a special case of Riemann Sums where the width of the rectangles used to find the area of a plane bound by a function and the x-axis are all of equal width.  Many examples are worked through. 

This is part 2 of my video "Area of a Plane w/ Rectangles & Limit of Infinite Sums" Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Definition of Area Riemann Sum Limit of Sums Part 2 of 2 Calculus 1

I show how the Definition of Area of a Plane is a special case of the Riemann Sum.  When finding the area of a plane bound by a function and an axis on a closed interval, the width of the partitions (probably rectangles) does not have to be equal.  I work through two examples that are related to each other.  The first examples has partitions with varying widths and the second with fixed widths.  I finish with giving the formal definition of Riemann Sum. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Riemann Sum Defined w/ 2 Limit of Sums Examples Calculus 1

In this example we find how fast water is rising in a conical tank when the level is 10 feet deep. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Calculus Related Rates Example Volume of Cone Calculus 1 AB

I work through five examples of finding REAL limits by analyzing graphs and numerical tables.  Infinite limits are not discussed in this video.  EXAMPLES AT 2:51 5:17 8:45 12:00 14:03 AP Calculus AB

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Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Finding Real limits Graphical & Numerical Approach Calculus 1 AB

I work through 3 more examples of Related Rates in Calculus.  The last to involve Angular Speed...or in other words...rate of change in theta.  Just a reminder for this lesson, Speed is the absolute value of velocity. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Related Rates Part 2 Linear vs Angular Speed Calculus 1 AB

NOTE:  I forgot a minus sine in the Sum and Difference rules. The right side should read f'(x)+or-g'(x).  Also, on the first page of notes it should read f'(x)=(1/5)x^(-4/5), I wrote x^(-4/5).  Annotation corrections are in the video, but not visible without Flash.  

I introduce the basic differentiation rules which include Constant Rule, Constant Multiple Rule, Power Rule, and Sum/Differece Rule.  Many examples are worked through the video.
Please help Close Caption this lesson
http://www.youtube.com/timedtext_vide...

Sending out a HUGE thank you to Rose Cabug for your help Close Captioning this math lesson... BAM!
Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Basic Differentiation Rules Calculus 1 AB

I explain how to find the domain values where a curve has a slope of zero using the first derivative.  I also explain how we can look at the sign changes of the first derivative to identify relative maximums and minimums.
ERROR NOTICE:  In the last example I only did solutions for x restricted to [0,2pi).  Without this restriction the solutions should have been expanded to include all possible solutions.  x=π/2+nπ, π/6+2nπ and 5π/6+2nπ.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Horizontal Tangent Lines and Differentiation Calculus 1 AB

EXAMPLES: 13:42 22:18 27:11 28:10 29:40
I explain the process of finding the lower and upper sums using Reimann Sums.  When a function is increasing, you use the left endpoints of rectangles to find the lower sum (under estimate the area) and the right endpoints of rectangles to find the upper sum (over estimate the area).  If a function is decreasing, the left end points will allow you to find the upper sums.  These sums estimate the area between a function and the x axis on a closed interval in my examples. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Estimating Area with Riemann Sums Finite Rectangles Calculus 1 AB

I introduce the Second Fundamental Theorem of Calculus.  I use three examples from my previous video "Definite Integral as a Function of X" to show you how the Second Fundamental Theorem of Calculus works.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Second Fundamental Theorem Calculus 1 AB

This math lesson about the Squeeze Theorem is an excerpt from my full length lesson Sequence in Calculus 11 Examples    • Sequences in Calculus 2 BC Converge o...  
A HUGE SHOUT OUT to my viewer OdysseyofNoises for Close Captioning this math lesson:D:D:D  You rock.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ 
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Squeeze Theorem for Sequences Sandwich Theorem Calculus 1

I work through two more examples of working through the chain rule.
Chain Rule with Trigonometric Functions 
   • Chain Rule with Trigonometric Functio...  
Chain Rule with Trig Functions Harder Examples 
   • Chain Rule with Trig Functions Harder...  
Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Chain Rule Harder Algebraic Examples Calculus 1 AB

EXAMPLES of Indefinite Integration 1:23 3:40
EXAMPLE of Definite Integration 7:18
EXAMPLE of Solving a Differential Equation 12:34

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Integration of Natural Exponential Functions Calculus 1 AB

EXAMPLES AT 5:42 11:17 18:44 27:58 35:23

Learning goals
1. Determine intervals on which a function is increasing or decreasing.
2. Apply the First Derivative Test to find relative extrema of a function.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

First Derivative Test Intervals of Increasing Decreasing & Relative Extrema Calculus 1 AB

I visually compare a function with it's first and second derivative to set up a future video introducing the second derivative test.  I discuss concavity and inflection point within this introduction Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Graphical Comparison Function to its 1st and 2nd Derivative Calculus 1 AB

I work through a problem showing how the Rolle's Theorem along with the Intermediate Value Theorem can prove that a function only has one real solution.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Application of Rolle's Theorem with Intermediate Value Theorem Calculus 1 AB

I explain how to find the derivative of functions that involve sine and cosine.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Derivatives with Sine and Cosine Calculus 1 AB

I work through examples of implicit differentiation at 0:36 4:38 8:14 .  This technique is required when you cannot get an equation into explicit form...or in other words " y in terms of x "
Finding the Second Derivative Implicitly    • Second Derivative Implicitly Calculus...  

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Implicit Differentiation 3  Examples Calculus 1 AB

I explain an example of finding an area in a plane defined by a function and the y axis within a closed interval.  At the beginning of the example at 1:53 I write deltaX, it should be deltaY. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Area  Against y Axis Riemman Limit of Sums Calculus 1

I introduce how to estimate a definite integral using the Trapezoidal Rule by using our knowledge of basic Geometry, give you the rule and then work through a second example using information from a table.  I also show how to determine if the Trapezoidal Rule will under or over estimate a definite integral at 21:02  I then introduce the Simpson's Rule and work through one more example.  

Example of Trapezoidal Rule at 7:06
Trapezoidal Rule Introduced at 17:16
Example of Trapezoidal Rule from a table at 23:23
Simpson's Rule introduced at 27:24  COPY ERROR.  Start of formula is (b-a)/3n
Simpson's Rule example at 33:54

Maximum Error in Trapezoidal Rule & Simpson's Rule 
   • Maximum Error in Trapezoidal Rule & S...  

Find the equation of a parabola given three points.
   • 3 Variable Systems: Parabola Equation...  

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at www.mathplane.com Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Trapezoidal Rule & Simpson's Rule Estimating Definite Integrals Calculus 1 AB READ DESCRIPTION

I introduce the Definite Integral, explain the definition, and work through an example of using the Definite Integral notation and Riemann Sum to find the area bound by a function and the x axis on a closed interval. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Definite Integrals Defined w. Riemann Limit of Sums Example Calculus 1 AB

I introduce the properties of limits that allow you to find the real limit of a function as x approaches "a" without needing to make a t-table or graph the function.  

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Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Properties of Limits Calculus 1 AB

I compare Implicit Differentiation to Explicit Differentiation.  Explicit differentiation requires that your equation is in the for of "y in terms of x".  When solving for y is not possible or very cumbersome you use Implicit Differentiation.
Please help Close Caption this lesson
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Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Introduction to Implicit Differentiation Calculus 1 AB

If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob   I explain how to determine if a function is even, odd, or neither and work through examples at  
Even Functions 3:39 5:03 8:33 10:42 11:23
Odd and Even Functions, or Neither 15:27 17:36 19:57 22:47 29:24
Please excuse the static from my mic.  I have made adjustments to avoid this in the future. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Even and Odd Functions Many Examples

I introduce the Summation Notation...Sigma...and work through five examples related to the topic of sequences.  I should be using the correct vocabulary of Sigma in this lesson instead "Greek E"

For all my lessons on Sequences and Series go here:)
http://www.profrobbob.com/pre-calculus/intro-to-sequences-arithmetic-geometric

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Summation Notation (Sigma)

I introduce and define the First Fundamental Theorem of Calculus.  I finish by working through 4 examples involving Polynomials, Quotients, Radicals, Absolute Value Function, and Trigonometric Functions.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

First Fundamental Theorem of Calculus Calculus 1 AB

I introduce the formulas for calculating the maximum expected error estimating a definite integral with the Trapezoidal Rule and Simpson's Rule.  Finish by working through four examples.
NOTE: There is an error calculating the maximum error with Simpson's Rule. At 9:36 I have 120/(1+3)^6 in the denominator, it should say 120/(1+2)^6.  Annotation corrections have been added.  My apologies.  
A HUGE SHOUT OUT to my viewer OdysseyofNoises for Close Captioning this math lesson:D:D:D
Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Maximum Error in Trapezoidal Rule & Simpson's Rule Calculus 1 AB READ DESCRIPTION

EXAMPLES at 7:14 10:34 16:40 21:47 25:36 27:58 34:00 36:59 38:42
After a short introduction I work through 8 examples of Integration of Natural Log Functions.  The 7 example is solving a differential equation and the last example is an example of a definite integral.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Integrating Natural Logarithm Function Calculus 1 AB

Visual Analysis 4:23 Examples at 21:40 29:47 42:16   Even though this is corrected, I still forgot the power of 2 on the cosine in the denominator at minute 46:41
I have a full set of notes for Concavity: Testing for Concavity, Look at some graphical examples of where concavity may change and where you may find Relative Maximums and Minimums, Graphically compare a function with it's First and Second Derivative, Define Point of Inflection, and finally the Second Derivative Test.  I then work through 3 examples of increasing difficulty.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Concavity Inflection Second Derivative Test 4 Examples Calculus 1 AB

Maximizing Volume of Cube w/fixed Surface Area 1:53
Maximizing Volume of Cone Inscribed in a Sphere 11:51
Minimizing Cost of Manufacturing a Storage Tank 25:03 Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Optimization Calculus Problems Minimizing Lengths
   • Optimization Calculus Problems Minimi...  
Optimization Cylinder in Sphere with Radius r
   • Optimization Cylinder in Sphere with ...  

Optimization Calculus Problems Volume Calculus 1 AB

I work through 4 examples of working with Definite Integrals that involve Common Geometric Areas.  These problems are easiest solved by first sketching the function and area of interest and then using geometry formula like area of a triangle to solve the definite integral. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Definite Integrals Common Geometric Area Calculus 1 AB

I introduce the precise Definition of a Limit and then work through three Epsilon Delta Proofs
Delta Epsilon Limit Proof involving a linear function at 11:31
Epsilon Delta Proof involving a quadratic function at 28:38
Epsilon Delta Proof involving an absolute value function at 47:29

Links to other lessons about Definition of a Limit
Lesson by Jatheen Varma Buddharaju
   • Calculus: Limits - Delta Epsilon proo...  
Lesson by Prof. Chuck Cunningham of James Madison University's Science & Math Learning Center (SMLC)   • 動画  
Lesson by Jatheen Varma Buddharaju Rational Function
   • Calculus: Limits: Rational polynomial...  
Lesson by Rootmath
   • 1.7 Proving a Limit: x^2 = 4 (advanced)  
Lesson by MathbyFives
   • Epsilon Delta Proof 2  

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Definition of a Limit Epsilon Delta Proof 3 Examples Calculus 1

I work through four examples of finding limits of piecewise functions using the properties of limits.  EXAMPLES 0:20 5:57 10:50 15:10 

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Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Limits of Piecewise Function Calculus 1 AB

Definition of Slope of a Tangent Line at a Point Examples 10:30 16:01 21:20
Slope of a Vertical Tangent Line Example 26:31
Derivative at a Sharp Bend Example 34:27
Definition of a Derivative Examples 46:20 49:43
Derivative at a Point of Discontinuity with Greatest Integer Function 54:39
Tangent Line Parallel to a Given Line 58:36
Tangent Line through a Point Not on the Curve 1:01:44

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Definition of Derivative & Tangent Line Problems Calculus 1 AB

I introduce how to estimate zeros using Newton's Method ( Newton-Raphson ) and work through three examples.
Estimating a Zero of a Function at 9:50
Estimating where two even functions intersect at 20:40
When Newton's Method fails at 27:51

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Newton's Method Linear Approximation Estimating a Zero of a Function Calculus 1 AB

I introduce Rolle's Theorem and work through two examples.  My first diagram in my explanation of Rolle's Theorem, should have labelled function f not g.  Part of the video was removed because you can see at 6:44 I wrote x as the square root of x squared, well that is equivalent to the absolute value of x.  This did not change my final answer, where is the tangent horizontal, but I inadvertently changed the function.  The correct process is displayed in the following scene.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Rolle's Theorem Calculus 1 AB

I do four example of finding derivatives using the chain rule with functions that involve trigonometric functions.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Chain Rule with Trig Functions Harder Examples Calculus 1 AB

I introduce finding the derivative of natural log functions.  I then work through 8 examples with increasing difficulty finishing with the last example that involves implicit differentiation.
EXAMPLES at 11:19 12:30 13:07 17:07 22:04 24:03 26:03 Implicit example 28:07

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Derivative of Natural Logarithm Functions Calculus 1 AB

I work through three examples at 0:21 8:21 11:28 of word problems that involve Indefinite Integration...or in other words finding antiderivatives. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Indefinite Integration Word Problems Calculus 1 AB

I introduce how definite integrals can allow us to find the displacement of a particle in linear motion and the total distance the particle travelled. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Definite Integration & Displacement and Total Distance of Linear Motion Calculus 1 AB

Example starts at 4:22  I work through finding the Domain, x-intercept, y-intercept, symmetry, horizontal asymptote, slant asymptote, vertical asymptote and holes, first derivative, intervals of increasing and decreasing, relative maximums and minimums, second derivative, intervals of concave up and down, and finally inflection points.  I then finally sketch the graph....phew! Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Summary of Curve Sketching Rational Function with Slant Asymptote Calculus 1 AB

I show you how to derive the differentiation rules for the "other" Trigonometric functions of tangent, secant, cosecant, and cotangent.

A HUGE SHOUT OUT to my viewer OdysseyofNoises for Close Captioning this math lesson:D:D:D Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Deriving Derivative Rules for Trigonometric Functions Tan, Cot, Sec, Csc Calculus 1 AB

I introduce the Mean Value Theorem in Calculus and work through an example.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Deriving Derivative Rules for Trigonometric Functions Tan, Cot, Sec, Csc Calculus 1 AB

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Calculus #13

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