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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 39e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 39e

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# Answer: Explain why or why not Determine whether the

ISBN: 9780321570567 2

## Solution for problem 39E Chapter 4.5

Calculus: Early Transcendentals | 1st Edition

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Problem 39E

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. The linear approximation to ?f?(?x?)= ?x?2 at the point (0, 0) is ?L?(?x?) = 0 b. Linear approximation provides a good approximation to ?f?(?x?)= | ?x? |at(0, 0). c. If ?f?(?x?) = ?mx? + ?b,? then at any point ?x? = ?a.? the linear approximation to ?f? is ?L?(?x?)= f?(?x?).

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Step 1 of 3

Solution 39E STEP 1 2 (a). The linear approximation to f(x) = x at the point (0, 0) is ) = 0. Let f be a function differentiable at an interval containing a point a.The linear approximation to f at a is given by L(x) = f(a)+f (a)(xa) Given f(x) = x and (a,f(a)) = (0,0) f(a) = 0. f(x) = 2x f (a) = 0 Therefore L(x) = 0 Thus the given statement is true. STEP 2 (b). Linear approximation provide s a d approximation to f (x)= | x | at(0, 0) .The linear approximation to f at a is given by L(x) = f(a)+f (a)(xa) Here f(x) = |x| is not differentiable at x=0. Therefore f(a) does not exist. Therefore the given statement is false. STEP 3 (c). If f(x) = mx + b, then at any point x = a. the linear approximation to f is L(x)= f(x). Given f(x) = mx+b and x=a. .The linear approximation to f at a is given by L(x) = f(a)+f (a)(xa) f(a) = ma+b Therefore f(x) = m f(a) = m Therefore L(x) = ma+b+m(xa) = ma+b+mxma = mx+b Thus the given statement is true,ie, L(x) = f(x)

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Step 3 of 3

##### ISBN: 9780321570567

This full solution covers the following key subjects: Approximation, Linear, point, good, explain. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The full step-by-step solution to problem: 39E from chapter: 4.5 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. The linear approximation to ?f?(?x?)= ?x?2 at the point (0, 0) is ?L?(?x?) = 0 b. Linear approximation provides a good approximation to ?f?(?x?)= | ?x? |at(0, 0). c. If ?f?(?x?) = ?mx? + ?b,? then at any point ?x? = ?a.? the linear approximation to ?f? is ?L?(?x?)= f?(?x?).” is broken down into a number of easy to follow steps, and 69 words. Since the solution to 39E from 4.5 chapter was answered, more than 354 students have viewed the full step-by-step answer.

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