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# Estimations with linear approximation Use linear

ISBN: 9780321570567 2

## Solution for problem 14E Chapter 4.5

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition

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Problem 14E

Estimations with linear approximation ?Use linear approximations to estimate the following quantities. Choose a value of a to produce a small error. tan 3°

Step-by-Step Solution:
Step 1 of 3

Solution 14E STEP 1 Linear approximation is a method of estimating the value of a function,f(x),near a point x=a,using the formula L(x) = f(a) + f a)(x a) STEP 2 Here,let f(x) = tan x ;and choose a=0 We get f () = sec x2 2 f(a) = tan 0 = 0and f (a = sec (0) = 1 Therefore the Linear approximation of the function,f(x),near a point x=a, is L(x) = f(a) + f a)(x a) = 0 + 1(x 0) = x L(x) = x STEP 3 According to the question tan 3 = tan( ) = f( ) {since 3 ( 60 60 ° degrees) means 60} f( ) L( ) 60 60 = 60= 0.0523 Therefore tan 3 0.0523

Step 2 of 3

Step 3 of 3

##### ISBN: 9780321570567

The full step-by-step solution to problem: 14E from chapter: 4.5 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. The answer to “Estimations with linear approximation ?Use linear approximations to estimate the following quantities. Choose a value of a to produce a small error. tan 3°” is broken down into a number of easy to follow steps, and 24 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: Linear, Approximation, choose, Error, estimate. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Since the solution to 14E from 4.5 chapter was answered, more than 361 students have viewed the full step-by-step answer.

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Estimations with linear approximation Use linear