Find the linearization L(x) of the function at a. f(x) = sin(x), a = π/6

Solution:

Linearization is an effective method for approximating the output of a function at any based on the value and slope of the function at , given that is differentiable on (or ) and that is close to .

It is given that

f(x) = sin (x)

By differentiating with respect to x

f’(x) = cos (x)

At a = π/6

y = f(π/6) = 1/2

f’(π/6) = √3/2

We know that the linearization is the tangent line

L(x) = f(x) + f’(a)(x - a)

Substituting the values

L(x) = 1/2 + √3/2 (x - π/6)

Therefore, the linearization L(x) of the function at a is L(x) = 1/2 + √3/2(x - π/6).

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Find the linearization L(x) of the function at a. f(x) = sin(x), a = π/6

Summary:

The linearization L(x) of the function at a f(x) = sin(x), a = π/6 is L(x) = 1/2 + √3/2(x - π/6).