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( أوراق عمل ملخص رااااائع لمادة التفاضل ) Calculus Derivatives and Limits Math Sheet
Limits Math Help
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'Hopital'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 Properites
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.
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( أوراق عمل ملخص رااااائع لمادة التفاضل ) Calculus Derivatives and Limits Math Sheet
Limits Math Help
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'Hopital'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 Properites
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.
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