Problem

Use Newton's method with the specified initial ap…

00:51

Problem 7 Easy Difficulty

Use Newton's method with the specified initial approximation $ x_1 $ to find $ x_3 $, the third approximation to the root of the given equation. (Give your answer to four decimal places.)

$ \dfrac{2}{x} - x^2 + 1 = 0 $, $ x_1 = 2 $

Answer

$$x_{3} \approx 1.5215$$

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

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Video Transcript

the first thing you can do is differentiate the equation we've been given, which gives us negative to overact squared minus two acts. Okay, now that we've got that, we know that when acts is two, we have 1.55 because we're using the formula Axe Marchioness to over acts minus X squared plus one divided by negative to over X squared minus two acts. Therefore, when X is 1.55 we have acts over here would be 1.5215

Amrita B.

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

Top Calculus 2 / BC Educators

Catherine R.

Missouri State University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Joseph L.

Boston College