# Calculus Derivatives and Limits Math Sheet

## An Engineers Quick Calculus Derivatives and Limits Reference

# Limits Math Help

## Definition of LimitReturn to Top

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 LimitReturn to Top

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

## Left Hand LimitReturn to Top

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

## Limit at InfinityReturn to Top

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 LimitsReturn to Top

Given the following conditions:

The following properties exist:

## Limit Evaluation at +-InfinityReturn to Top

## Limit Evaluation MethodsReturn to Top

### Continuous FunctionsReturn to Top

If f(x) is continuous at a then:

### Continuous Functions and CompositionsReturn to Top

If f(x) is continuous at b:

### Factor and CancelReturn to Top

### L'Hospital's RuleReturn to Top

# Derivatives Math Help

## Definition of a DerivativeReturn to Top

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

## Mean Value TheoremReturn to Top

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

## Basic ProperitesReturn to Top

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

## Product RuleReturn to Top

The product rule applies when differentiable functions are multiplied.

## Quotient RuleReturn to Top

Quotient rule applies when differentiable functions are divided.

## Power RuleReturn to Top

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

## Chain RuleReturn to Top

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

## Common DerivativesReturn to Top

## Chain Rule ExamplesReturn to Top

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