Linear Approximation Calculator

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 For a given value, the approximate value the function approaches for that value is called as the Linear

approximation. Linear approximation is calculated by the linear approximation formulaf(x) = f(x0) + f'(x0) (x –

x0). The online tool used to calculate the linear approximation using the linear approximation formula is called

as linear approximation calculator.



Example 1: Find the linear approximation f(x) = 3x2 when x tends to 4.


Given f(x) = 3x2 and the x approaches 4;

x0 = 4; f(4) = 3 * 42 = 48.

f'(x) = 6x <- f'(4) = 6*4 = 24.

Linear approximation formula f(x) = f(x0) + f'(x0) (x –x0)

f(x) =  48 + 24(x - 4)

f(x) = 48 + 24x - 96

f(x) = 24 x - 48.

Liner approximation of f(x) = 24 x - 48.



Example 2: Find the linear approximation f(x) = 2x + 1 when x tends to 3

Given f(x) = 2 x + 1 and the x approaches 3.

<-x0 = 3 <-f(3) = 2*3 + 1 = 7.

<-f'(x) = 2<- f'(3) = 2.

Linear approximation formulaf(x) = f(x0) + f'(x0) (x –x0)

<-f(x) =  7 + 2(x - 3)

<-f(x) = 7 + 2 x - 6;

f(x) = 2x + 1

Liner approximation of f(x) = 2x + 1.
 

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