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Definition of Limit
Right Hand Limit
Left Hand Limit
Limit at Infinity
Properties of Limits
Limit Eval. at +-Infinity
Limit Evaluation Methods
Continuous Functions
Continuous F&C.
Factor and Cancel
L'Hospital's Rule
Definition of a Derivative
Mean Value Theorem
Basic Properites
Product Rule
Quotient Rule
Power Rule
Chain Rule
Common Derivatives
Chain Rule Examples
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.
The following expression states that as x approaches the value c and x > c the function approaches the value L.
The following expression states that as x approaches the value c and x < c the function approaches the value L.
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.
Given the following conditions:
The following properties exist:
If f(x) is continuous at a then:
If f(x) is continuous at b:
The derivative is way to define how an expressions output changes as the inputs change. Using limits the derivative is defined as:
This is a method to approximate the derivative. The function must be differentiable over the interval (a,b) and a < c < b.
If there exists a derivative for f(x) and g(x), and c and n are real numbers the following are true:
The product rule applies when differentiable functions are multiplied.
Quotient rule applies when differentiable functions are divided.
The power rule applies when a differentiable function is raised to a power.
The chain rule applies when a differentiable function is applied to another differentiable function.
These are some examples of common derivatives that require the chain rule.
