3.8 Newton’s Method How do you find a root of the following function without a graphing calculator? This is what Newton did.

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3.8 Newton’s Method How do you find a root of the following function without a graphing calculator? This is what Newton did.

Let’s begin with this: Example 1: Calculate the first three approximations x1, x2, x3 to a root of f(x) = x2 – 5 using the initial guess x0 = 2. (means approximating )

Example 2: Calculate 3 iterations of Newton’s Method to approximate zero.

Example 3: Show that the following function has four real roots with x0 = 0, Newton’s Method converges to the root near -2. x0 = -1, Newton’s Method converges to the root near -1.