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485 resources with the keyterm Calculus

Videos (Over 2 Million Educational Videos Available)
Ancient Egypt | What Everyday Life Was Actually Like Video
9:28
Ancient Egypt | What Everyday Life Was...
Cells - Overview & Introduction Video
4:07
Cells - Overview & Introduction
Defining Gravity Video
3:11
Defining Gravity
Other Resource Types (485)
9:44
Lesson Planet

Introduction to Rate-of-Change Problems

For Students 11th - Higher Ed
Sal solves an example for finding the rate of change of the height of water in a cone at a specific point when it is being filled at a given rate. In this video, Sal reviews the volume of a cone and the chain rule and then, uses these to...
9:37
Lesson Planet

Maxima Minima Slope Intuition

For Students 11th - Higher Ed
Before solving any problems, Sal gives an overview of what happens to the slope, first derivative, and second derivative at local maxima and minima to give the viewer a more intuitive feel for these types of problems.
9:49
Lesson Planet

Optimization Example 4

For Students 11th - Higher Ed
Sal does another optimization example, this time, minimizing the total cost of an open rectangular box. In this problem, the volume can be defined in terms of a single variable and given a cost model, he builds a cost equation. He finds...
9:44
Lesson Planet

Graphing with Calculus

For Students 11th - Higher Ed
In a problem where you are not given the original function, but rather only three known points on the graph and a few additional pieces of information about when the first and second derivatives are positive or negative, Sal shows how...
17:30
Lesson Planet

Optimization with Calculus 3

For Students 11th - Higher Ed
Using what one learned about finding the minimum and maximum of functions, the optimization problem to find two numbers whose product is -16 and whose sum of squares is a minimum is solved. Sal starts by writing the equations and...
7:03
Lesson Planet

Proof: d/dx(x^n)

For Students 11th - Higher Ed
Using the binomial theorem and definition of a limit, Sal shows a proof that the derivative of xn equals nxn-1.
5:07
Lesson Planet

Proof: d/dx(sqrt(x))

For Students 11th - Higher Ed
Using the definition of a limit, Sal proves the derivative of �x or x1/2 is equal to _ x-1/2.
9:52
Lesson Planet

Proof: d/dx(ln x)=1/x

For Students 11th - Higher Ed
Using the definition of a limit, various properties of logarithms, and a definition of e, Sal shows the proof of derivative of ln x = 1/x. Note: The video titled "Proof of Derivatives of Ln(x) and e^x,Ó has a clearer explanation of this...
4:40
Lesson Planet

Proof: d/dx(e^x) = e6x

For Students 11th - Higher Ed
Using the derivative of ln x, the chain rule, and the definition of a limit, Sal shows a proof that derivative of ex = ex. Note: The video titled "Proof of Derivatives of Ln(x) and e^x,Ó has a clearer explanation of this proof.
8:08
Lesson Planet

Equation of a Tangent Line

For Students 11th - Higher Ed
Using a specific example, Sal shows how to find the equation of a tangent line to a given function at a specific point. Specifically, he solves the problem of finding the tangent line to the function f(x) = xex at x = 1. This problem...
9:50
Lesson Planet

Calculus: Derivatives 3

For Students 11th - Higher Ed
This video covers the differential notation dy/dx and generalizes the rule for finding the derivative of any polynomial. It also extends the notion of the derivatives covered in the Khan Academy videos, "Calculus Derivatives 2Ó and...
9:30
Lesson Planet

Calculus: Derivatives 2

For Students 11th - Higher Ed
Sal continues where he left off with the last video, "Derivatives 1,Ó by looking at the equation y = x^2 and examining the slope of the secant line at a specific point, and again defining the limit as x approaches zero to get the slope...
11:05
Lesson Planet

Calculus: Derivatives 2.5 (new HD version)

For Students 11th - Higher Ed
By defining the formal definition of a derivative, f�(x), Sal is able to find the general form of the derivate function for the example f(x) = x2. He continues to stress the importance of an intuitive understanding of derivative functions.
8:28
Lesson Planet

Calculus: Derivatives 2 (new HD version)

For Students 11th - Higher Ed
Sal continues where he left off with the last video, "Derivatives 1,Ó by looking at the equation y = x2 and examining the slope of the secant line at a specific point. He continues with defining the limit as x approaches zero to get the...
9:26
Lesson Planet

Calculus: Derivatives 1

For Students 11th - Higher Ed
Sal defines the term derivative by taking the listener on a well-organized tour of slope. First, he reviews the concept of slope of a line from algebra, then extends this idea to look at the slope of the curve by first examining a secant...
15:43
Lesson Planet

Calculus: Derivatives 1 (new HD version)

For Students 11th - Higher Ed
Sal defines the term derivative by taking the listener on a well-organized tour of slope. First, he reviews the concept of slope of a line from algebra, then extends this idea to look at the slope of the curve by first examining a secant...
9:02
Lesson Planet

Calculus: Derivative of x^(x^x)

For Students 11th - Higher Ed
Sal starts with an example of finding dy/dx of y = x2 and builds to showing the solution to the more complicated implicit differentiation problem of finding the derivative of y in terms of x of y = x ^ x ^ x .
16:48
Lesson Planet

Mean Value Theorem

For Students 11th - Higher Ed
Sal spends most this video explaining what the Mean Value Theorem says in a very intuitive way. He follows this with a concrete example of finding the value of a function on a closed interval where the slope is the same as the average...
12:27
Lesson Planet

Proofs of Derivatives of Ln(x) and e6x

For Students 11th - Higher Ed
In this video, Sal takes on the challenge of proving both the derivative of ln x = 1/x and of ex = ex, showing that no circular logic is used in the proof.  It contains a clearer version of both proofs shown in the videos titled, _Proof...
8:39
Lesson Planet

Proof: d/dx(e^x) = e6x

For Students 11th - Higher Ed
Using the derivative of ln x, the chain rule, and the definition of a limit, Sal shows a proof that derivative of ex = ex. Note: The video titled �Proof of Derivatives of Ln(x) and e^x,� has a clearer explanation of this proof.
8:49
Lesson Planet

Product Rule

For Students 11th - Higher Ed
Sal defines the product rule and then shows two examples of how it is used. He then shows an example of finding the derivative by using both the chain rule and product rule together.
Lesson Planet

Calculus 2.1 day 2 - Step Functions

For Teachers 11th - 12th
"Step functions" are sometimes used to describe real-life situations. This extensive lesson with many practice examples demonstrates two such functions: the Greatest Integer Function and the Least Integer Function. The commands on the...
Lesson Planet

Calculus 3.6 - The Chain Rule

For Teachers 11th - 12th
Greg Kelly puts together another great slide presentation to demonstrate ways to combine derivative rules to evaluate more complicated functions. This pattern is called the chain rule.  He shows step by step ways to solve these...
Lesson Planet

Drawing a Line Tangent to a Circle

For Teachers 9th - 12th Standards
Explore lines tangent to a circle. In this math lesson, students manipulate circles and lines on a TI calculator. They draw a circle  and analyze perpendicular lines intersecting the circle in only one place. This activity works best if...