"Find the linear approximation of the function f(x)=4−x..." was answered by our community

oliviayychengwh

Answered question

2021-12-18

Find the linear approximation of the function

f (x) = \sqrt{4 - x}

at

a = 0

and use it to approximate the numbers

\sqrt{3.9}

and

\sqrt{3.99}

, please.

Answer & Explanation

enhebrevz

Beginner2021-12-19Added 25 answers

Use the Taylor Form:

f (x) = f (a) + (x - a) \times f^{'} (a) \dots

f (x) = {(\sqrt{4 - x})}^{'} = \frac{1}{2} \times \frac{- 1}{\sqrt{4 - x}}

f (0) = \sqrt{4 - 0} = 2

f^{'} (0) = \frac{1}{2} \times \frac{- 1}{\sqrt{4}} = - \frac{1}{4}

\sqrt{3.9} = f (x) \approx 2 + 0.1 (- \frac{1}{4}) = 1.9750

\sqrt{3.99} = f (x) \approx 2 + 0.01 (- \frac{1}{4}) = 1.9975

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