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# Find the linearization l(x) of the function at a. f(x) = x^{1/2}, a = 4

**Solution:**

Given, the function f(x) = x^{1/2}

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) = x^{1/2}

f(a) = f(4) = 2

f’(x) = 1/2 x ^{-½}

= 1/2√x

f’(a) = f’(4) = 1/4

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

L(x) = 2 + (1/4)(x - 4)

Therefore, the linearization of f(x) = x^{1/2} at a = 4 is L(x) = 2 + (1/4)(x - 4).

## Find the linearization l(x) of the function at a. f(x) = x^{1/2}, a = 4

**Summary:**

The linearization of the function f(x) = x^{1/2} at a=4 is L(x) = 2 + (1/4)(x - 4).

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