Question

Use the Error Bound to find the least possible value of N for which Error(SN) ≤ 1 × 10^(-9) in approximating ∫10^6 e^(x^2) dx using the result that Error(SN) ≤ K4(b - a)^5 / (180N^4), where K4 is the least upper bound for all absolute values of the fourth derivatives of the function 6e^(x^2) on the interval [a, b]. N =

Name: use the error bound to find the least possible value of n for which errorsn1109 in approximating 106ex2dx using the result that errorsnk4ba5180n4 where k4 is the least upper bound for all ab 60723
Uploaded: 2023-09-14T08:24:03-08:00
Duration: 7 min 9 s
Channel: Adi S
Description: use the error bound to find the least possible value of n for which errorsn1109 in approximating 106ex2dx using the result that errorsnk4ba5180n4 where k4 is the least upper bound for all ab 60723

          Use the Error Bound to find the least possible value of N for which Error(SN) ≤ 1 × 10^(-9) in approximating ∫10^6 e^(x^2) dx using the result that Error(SN) ≤ K4(b - a)^5 / (180N^4), where K4 is the least upper bound for all absolute values of the fourth derivatives of the function 6e^(x^2) on the interval [a, b].
N =

Added by Cynthia M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/14/2023

Step 1

First, we need to find the least upper bound for all absolute values of the fourth derivatives of the function $6e^{x^2}$ on the interval $[a, b]$. The function is $f(x) = 6e^{x^2}$. Let's find its fourth derivative: $f'(x) = 12xe^{x^2}$ $f''(x) = 12e^{x^2} + Show more…

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Use the Error Bound to find the least possible value of N for which Error(SN) ≤ 1 × 10^(-9) in approximating ∫10^6 e^(x^2) dx using the result that Error(SN) ≤ K4(b - a)^5 / (180N^4), where K4 is the least upper bound for all absolute values of the fourth derivatives of the function 6e^(x^2) on the interval [a, b]. N =