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0021/01/01
calculus derivatives and limits

https://www.eeweb.com/tools/calculus-derivatives-and-limits-reference-sheet

#### Definition of Limit

The limit is a method of evaluating an expression as an argument approaches a value. This value can be any point on the number line and often limits are evaluated as an argument approaches infinity or minus infinity. The following expression states that as x approaches the value c the function approaches the value L.

#### Right Hand Limit

The following expression states that as x approaches the value c and x > c the function approaches the value L.

#### Left Hand Limit

The following expression states that as x approaches the value c and x < c the function approaches the value L.

#### Limit at Infinity

The following expression states that as x approaches infinity, the value c is a very large and positive number, the function approaches the value L.

Also the limit as x approaches negative infinity, the value of c is a very large and negative number, is expressed below.

#### Properties of Limits

Given the following conditions:

The following properties exist:

#### Limit Evaluation Methods

##### Continuous Functions

If f(x) is continuous at a then:

##### Continuous Functions and Compositions

If f(x) is continuous at b:

#### Definition of a Derivative

The derivative is way to define how an expressions output changes as the inputs change. Using limits the derivative is defined as:

#### Mean Value Theorem

This is a method to approximate the derivative. The function must be differentiable over the interval (a,b) and a < c < b.

#### Basic Properties

If there exists a derivative for f(x) and g(x), and c and n are real numbers the following are true:

#### Product Rule

The product rule applies when differentiable functions are multiplied.

#### Quotient Rule

Quotient rule applies when differentiable functions are divided.

#### Power Rule

The power rule applies when a differentiable function is raised to a power.

#### Chain Rule

The chain rule applies when a differentiable function is applied to another differentiable function.

#### Chain Rule Examples

These are some examples of common derivatives that require the chain rule.

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