Find the linear approximation of the function f(x) = 1 - x at a = 0

Solution:

Linearization is a mathematical process of determining the linear approximation of inputs and corresponding outputs.

Given, the function f(x) = 1 - x

We have to find the linearization L(x) of the function at a =0.

Using the formula,

L(x) = f(a) + f’(a)(x - a)

Now,

f(x) = 1 - x

f(a) = f(0) = 1

f’(x) = -1

f’(a) = f’(0) = -1

Substituting the values of f(a) and f’(a), the function becomes

L(x) = 1 + (-1) (x - 1)

Therefore, the linearization of f(x) = 1 - x at a = 0 is L(x) = 1 - 1 (x - 1).

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Find the linear approximation of the function f(x) = 1 - x at a = 0

Summary:

The linearization of the function f(x) = 1 - x at a=0 is L(x) = 1 - 1 (x - 1).