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 at +-Infinity
Limit Evaluation Methods
Continuous Functions
If f(x) is continuous at a then:
Continuous Functions and Compositions
If f(x) is continuous at b:
Factor and Cancel
L’Hospital’s Rule
Derivatives Math Help
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.
Common Derivatives
Chain Rule Examples
These are some examples of common derivatives that require the chain rule.
