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'Hopital'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.