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(a) Define ƒ (x) := √² -²/2 dt 0.45. √2π Using the Fundamental Theorem of Calculus, write down Newton's method applied to f.

(a) Define ƒ (x) := √² -²/2 dt 0.45. √2π Using the Fundamental Theorem of Calculus, write down Newton's method applied to f.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Newton's method

[8] **Computational exercise** Consider the nonlinear equation for \( x \): \[ \int_{0}^{x} \frac{1}{\sqrt{2\pi}} e^{-t^2/2} \, dt = 0.45. \] Note that \( t \) is just a ‘dummy’ variable of integration.
Transcribed Image Text:[8] **Computational exercise** Consider the nonlinear equation for \( x \): \[ \int_{0}^{x} \frac{1}{\sqrt{2\pi}} e^{-t^2/2} \, dt = 0.45. \] Note that \( t \) is just a ‘dummy’ variable of integration.
(a) Define \( f(x) := \int_0^x \frac{1}{\sqrt{2\pi}} e^{-t^2/2} \, dt - 0.45. \) Using the Fundamental Theorem of Calculus, write down Newton’s method applied to \( f \).
Transcribed Image Text:(a) Define \( f(x) := \int_0^x \frac{1}{\sqrt{2\pi}} e^{-t^2/2} \, dt - 0.45. \) Using the Fundamental Theorem of Calculus, write down Newton’s method applied to \( f \).
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