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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).
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).
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