Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
4th Edition
ISBN: 9780133178579
Author: Ross L. Finney
Publisher: PEARSON
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Limits
When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…
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Chapter 5.6, Problem 1QQ
To determine

To find: the third approximation x3 if the first approximation is x1=1 .

Expert Solution & Answer
Check Mark

Answer to Problem 1QQ

The third approximation is B-0.465.

Explanation of Solution

Given information:

The real root is x3+2x−1=0 .

Formula used:

Newton’s method:

  xn+1=xn−f(xn)f'(xn)

Calculation :

We have to find the third approximation x3 if the first approximation is x1=1 .

  Let, f(x)=x3+2x−1Then, f'(x)=3x2+2andxn+1=xn−f(xn)f'(xn)x1+1=x1−f(x1)f'(x1)x2=1−x3+2x−13x2+2       [Since x1=1]x2=1−(1)3+2(1)−13(1)2+2x2=1−1+2−13+2x2=1−25x2=5−25=35

Again, use Newton’s method to find the third approximation,

  xn+1=xn−f(x)f'(x)

Therefore,

  x3=x2−f(x2)f'(x2)x3=35−(35)3+2(35)−13(35)2+2       [Put the value of x2=35]x3=35−27125+65−13(925)+2       [Use a calculator.]x3=35−0.216+1.2−12725+2x3=35−0.216+1.2−11.08+2x3=35−0.4163.08x3=0.6−0.135x3=0.465

The third approximation is B-0.465.

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Chapter 5.6, Problem 47E
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Chapter 5.6, Problem 2QQ

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

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