Question

For approximately what values of x can you replace sin x by $x - \frac{x^3}{6}$ with an error of magnitude no greater than $7 \times 10^{-3}$? $|x| < \Box$ (Round to five decimal places.)

Name: for approximately what values of x can you replace sin x by x fracx36 with an error of magnitude no greater than 7 times 10 3 x box round to five decimal places 70443
Uploaded: 2020-02-24T22:24:24-08:00
Duration: 3 min 41 s
Channel: Linh Vu
Description: for approximately what values of x can you replace sin x by x fracx36 with an error of magnitude no greater than 7 times 10 3 x box round to five decimal places 70443

          For approximately what values of x can you replace sin x by $x - \frac{x^3}{6}$ with an error of magnitude no greater than $7 \times 10^{-3}$?
$|x| < \Box$
(Round to five decimal places.)

$for approximately what values of x can you replace sin x by x fracx36 with an error of magnitude no greater than 7 times 10 3 x box round to five decimal places 70443$

Added by Steve L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Linh Vu

02/24/2020

Step 1

The error of this approximation is given by the magnitude of the first neglected term in the Taylor series. In this case, the first neglected term is $\frac{x^5}{5!}$. So, the error is approximately $E(x) = \left| \frac{x^5}{5!} \right|$. We are given that the Show more…

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For approximately what values of x can you replace sin x by $x - \frac{x^3}{6}$ with an error of magnitude no greater than $7 \times 10^{-3}$? $|x| < \Box$ (Round to five decimal places.)