Calculus 1

Maximum and minimum

Introduction:

Functions can achieve maximum and minimum values in an interval or in it's entire domain. An easy way to locate these maximums and minimums is by using the first and second derivative

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If a function has a maximum or a minimum, it can be found my inspecting the first derivative. A maximum or minimum can happen at any of these these places

Calculus 1

Implicit Differentiation is a way to take derivatives when your function is not of the form y = "expression of one variable". It is a application of the chain rule, and can make differentiation much simpler.

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Whenever you implicitly differentiate you have to pay attention to the different variables. If you are taking the derivative with respect to x, and the term has an x in it, you do the regular derivative.

If the term has another variable instead of x, for example y. You take the derivative with respect to y, then multiply it by dy/dx.

In essence, it's just one extra step of multiplying the derivative by dy/dx.

Once you have finished doing this, you gather dy/dx to one side of the equation, and that is the derivative y with respect to x.

Note:

Calculus 1

The Chain Rule

Introduction:

This video tutorial teaches us the chain rule. It's the most powerful derivative tool that you have, and it is heavily used.

Information covered in video:

Chain Rule, Chain rule with "U" substitution

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The chain rule is used to take the derivative of a function that depends on another function. These functions are called composite functions. Whenever the inside function is something more complicated than x, the chain rule is needed.

Calculus 1

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Limit Definition of Derivative

Introduction:

This video shows how to take derivatives using the limit definition of derivative.

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A derivative is a rate of change of a function or a graph. We can find this derivative by using a tangent line to the point. By taking the limit has h --> 0, we check the slope of the graph as we make the x distance smaller and smaller.

My main warning is to use your parenthesis as you work these out.

Calculus 1

coming soon - series

Introduction:

Coming soon - Series and Riemann Sums

Calculus 1

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Evaluating limits Intermediate

Introduction:

This video tutorial covers how to take the limits of undeterminable form 0 divided by 0.

Information covered in video:

Factoring, algebra, L'Hopital's Rule

Video Upload:

eval limits function int_39.mp4

When we are faced with a limit of the undeterminable form something divided by 0, we can use different methods to get the answer.

1. We can factor out the denominator so that we no longer get zero on the bottom.

2. We can use L'Hoptal's rule and plug our number into the derivative.

3. We can use algebra, and our knowledge of fractions to get the zero out of the denominator.

Using these methods will help us to handle limits that are of the undeterminable form 0/0 or someone divided by 0.

Calculus 1

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Evaluating limits basic

Introduction:

This video tutorial covers how to evaluate limits of functions and definition of infinity.

Information covered in video:

Something being divided by 0, Undefined limits, Limit from left, limit from right, overall limit, plugging in limits, value, infinity.

Video Upload:

eval limits function_38.mp4

How do I find the limit of a function?

If the function is continuous around our area of interest, then in a simple example we can find the limit by plugging in the value that the function is approaching. If we get an undeterminable form, then we have to use simplification tricks before we find our limit.

What is an undeterminable form?

1. Anything divided by 0

2. Infinity Divided by infinity

3. 0 raised to the 0 power.

4. zero times infinity

Calculus 1

Intro to limits with graphs

Introduction:

This video tutorial covers how to take the overall limit by examining graphs..

Information covered in video:

Undefined limits, Limit from left, limit from right, overall limit, limits approaching infinity

Video Upload:

Limits graphs_371_0.mp4

A Limit is the value that a graph or a function approaches near a certain point of interest. When we take the limit, we are not concerned about what actually happens a the point of interest. We are only concerned about what happens to the right and to the left of the point of interest. That information alone is enough to determine the limit. When does the limit exist? When we examine the graph, and the value that to the left and to the right of the point of interest agree, the limit exists.