how to do limits in calculus

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How to do limits in Calculus

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How to do Limits in Calculus : 

How to do Limits in Calculus

The Derivate of a Function : 

The Derivate of a Function Limits is the study of Calculus and it is used for defining some of the most important concepts in Calculus – continuity, the derivate of a function and definite integral of a function.

Example of limits : 

Example of limits 2 Find lim (5 + X) X Substitute 2 in x 5 + 2 = 7

Another Example of Limits : 

Another Example of Limits 3 Find lim (5x - 4 – x2) X Substitute 3 in X 15 – 4 – 32 15 – 4 – 9 11 – 9 2

Another Example in Limits : 

Another Example in Limits Find Substitute 2 in X 3 = 0 It’s zero and does not exist.

Another Example of Limits : 

Another Example of Limits Find 2 + 2 = 4 Substitute 2 into x Simplify the top x2 - y2 = (x+y) (x- y) Find like terms and cancel it

Definition of F differentiable at a : 

Definition of F differentiable at a For any function f and any point x = a If the following limit exist The shorter way can be written as

Definition of F differentiable at a Continue : 

Definition of F differentiable at a Continue Can be written as f ’(a) And as This means derivate a

Example of Derivate : 

Example of Derivate Find the derivative of y = (2x +1)2 at x = 3 Square of Binomial (a + b)2 = a2 + 2ab +b2 y = 4x2 + 4x + 1 y = 8x +4 y = 8(3) + 4 y = 24 + 4 y = 28 Substitute 3 into x

Another Example of Derivate : 

Another Example of Derivate Find the derivate of y = (2x + 1)2 (a + b)2 = a2 + 2ab + b2 At a point x = a y = 4x2 + 4x + 1 y = 8x + 4 y = 8a + 4 y = 8a + 4 Substitute a into x Simplify