Question

Use Newton's method to approximate all intersection points of the following pair of curves.

Round to six decimal places as needed.

Step 1

Before we get into the solution of the question, let's understand a bit about Newton's method.

If x_{n} is an approximate solution of F(x) and F’(x_{n}) ≠ 0 then the next approximate solution, x_{n+1} is given by the expression on the White Board.

Step 2

Step 3

Based on the pair of curves given to us, let's define F(x) as:

F(x) = 1/x – (36 – 16x2) = 16x2 - 36 + 1 /x

Hence, F'(x) = 32...

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