Question

Estimate the error if $P_2(x) = 1 - \frac{x^2}{2}$ is used to estimate the value of $\cos x$ at $x = 0.9$. $|\text{Error}| < \boxed{\phantom{0}}$ (Simplify your answer. Round to seven decimal places as needed.)

Name: estimate the error if p2x 1 fracx22 is used to estimate the value of cos x at x 09 texterror boxedphantom0 simplify your answer round to seven decimal places as needed 23384
Uploaded: 2023-02-19T06:00:44-08:00
Duration: 2 min 1 s
Channel: Sri K
Description: estimate the error if p2x 1 fracx22 is used to estimate the value of cos x at x 09 texterror boxedphantom0 simplify your answer round to seven decimal places as needed 23384

          Estimate the error if $P_2(x) = 1 - \frac{x^2}{2}$ is used to estimate the value of $\cos x$ at $x = 0.9$.
$|\text{Error}| < \boxed{\phantom{0}}$ (Simplify your answer. Round to seven decimal places as needed.)

$estimate the error if p2x 1 fracx22 is used to estimate the value of cos x at x 09 texterror boxedphantom0 simplify your answer round to seven decimal places as needed 23384$

Added by Joshua S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

02/19/2023

Step 1

9$. The Taylor series for $\cos x$ centered at $a=0$ (Maclaurin series) is given by: $\cos x = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!} = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \dots$ The given polynomial $P_2(x) = 1 - \frac{x^2}{2}$ is the Show more…

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Estimate the error if $P_2(x) = 1 - \frac{x^2}{2}$ is used to estimate the value of $\cos x$ at $x = 0.9$. $|\text{Error}| < \boxed{\phantom{0}}$ (Simplify your answer. Round to seven decimal places as needed.)