Get solution: Show that each of the following equations has a unique solution in the

Chapter 1, Problem 8

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QUESTION:

Show that each of the following equations has a unique solution in the given interval, and use Newton's method to find it to 5 significant decimal places.

 

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QUESTION:

Show that each of the following equations has a unique solution in the given interval, and use Newton's method to find it to 5 significant decimal places.

 

ANSWER:

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Step 1 of 6

First prove that the given function has a unique solution.

Let the given function be

To prove that f has a unique solution in (0,1), to prove that f is continuous, monotone and changes its sign at the end of the interval (0,1).

Since f is a linear combination of  and a function of x, f(x) is continuous.

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