Question

Let $f(x) = \sin(x)$ and $x_0 = \frac{\pi}{4}$. Find the smallest positive integer $n$ such that the remainder formula for the Taylor approximation guarantees that the absolute value of the remainder is less than $10^{-6}$ for all $x \in [0, \frac{\pi}{4}]$.

Name: let fx sinx and x0 fracpi4 find the smallest positive integer n such that the remainder formula for the taylor approximation guarantees that the absolute value of the remainder is less than 31558
Uploaded: 2022-04-20T03:55:10-08:00
Duration: 1 min 23 s
Channel: Gio Maya
Description: let fx sinx and x0 fracpi4 find the smallest positive integer n such that the remainder formula for the taylor approximation guarantees that the absolute value of the remainder is less than 31558

          Let $f(x) = \sin(x)$ and $x_0 = \frac{\pi}{4}$.

Find the smallest positive integer $n$ such that the remainder formula for the Taylor approximation guarantees that the absolute value of the remainder is less than $10^{-6}$ for all $x \in [0, \frac{\pi}{4}]$.

$let fx sinx and x0 fracpi4 find the smallest positive integer n such that the remainder formula for the taylor approximation guarantees that the absolute value of the remainder is less than 31558$

Added by Dana A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Gio Maya

04/20/2022

Step 1

Step 1: The remainder formula for the Taylor approximation is given by $$R_n(x) = \frac{f^{(n+1)}(c)}{(n+1)!}(x-x_0)^{n+1}$$ where $c$ is some value between $x$ and $x_0$. Show more…

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Let $f(x) = \sin(x)$ and $x_0 = \frac{\pi}{4}$. Find the smallest positive integer $n$ such that the remainder formula for the Taylor approximation guarantees that the absolute value of the remainder is less than $10^{-6}$ for all $x \in [0, \frac{\pi}{4}]$.