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Elementary Calculus Limits, Analytic Geometry, and Approximations Newton's Method Examples Example 1: Approximating a Zero
 

Example 1: Approximating a Zero

Approximate a zero of f(x) = x3 + 2x2 - 5 by Newton's method.

Step 1

The graph is shown in Figure 5.9.4. We choose x1 = 1 as our first approximation.

Step 2

f'(x) = 3x2 + 4x

Step 3

05_limits_g_approx-441.gif

Step 4

05_limits_g_approx-443.gif

05_limits_g_approx-442.gif

Figure 5.9.4

 

As a check we compute

f(x3) = x33 + 2x32 - 5 ~ 0.01

One more iteration gives much more accuracy:

05_limits_g_approx-444.gif

Last Update: 2006-Nov-15