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Find the linear approximation of the function f(x) = √25-x at a = 0 and use it to approximate the numbers √24.9 and √24.99. L(x) = 5 -0.1x √24.9 2.51 √24.99 = 2.501 X X

Find the linear approximation of the function f(x) = √25-x at a = 0 and use it to approximate the numbers √24.9 and √24.99. L(x) = 5 -0.1x √24.9 2.51 √24.99 = 2.501 X X

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the linear approximation of the function \( f(x) = \sqrt{25-x} \) at \( a = 0 \) and use it to approximate the numbers \( \sqrt{24.9} \) and \( \sqrt{24.99} \). \[ L(x) = 5 - 0.1x \] (This is marked as correct.) For calculations: - \( \sqrt{24.9} \approx 2.51 \) (This is incorrect.) - \( \sqrt{24.99} \approx 2.501 \) (This is incorrect.)
Transcribed Image Text:Find the linear approximation of the function \( f(x) = \sqrt{25-x} \) at \( a = 0 \) and use it to approximate the numbers \( \sqrt{24.9} \) and \( \sqrt{24.99} \). \[ L(x) = 5 - 0.1x \] (This is marked as correct.) For calculations: - \( \sqrt{24.9} \approx 2.51 \) (This is incorrect.) - \( \sqrt{24.99} \approx 2.501 \) (This is incorrect.)
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