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Home Limits, Analytic Geometry, and Approximations Newton's Method Examples Example 3: Approximating an Intersection of Two Graphs  
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Example 3: Approximating an Intersection of Two Graphs
Approximate the point x where sin x = ln x. As one can see from the graphs of sin x and In x in Figure 5.9.6, sin x and ln x cross at one point x, which is somewhere between x = 1 (where ln x crosses the xaxis going up) and x = π (where sin x crosses the xaxis going down). To apply Newton's method, we let f(x) be the function f(x) = sin x  ln x shown in Figure 5.9.7. We wish to approximate the zero of f(x). Figure 5.9.6 Figure 5.9.7
The answer is x ~ 2.219107150. On a calculator we find that sin (2.219107150) = 0.797104929 ln (2.219107150) = 0.797104930.


Home Limits, Analytic Geometry, and Approximations Newton's Method Examples Example 3: Approximating an Intersection of Two Graphs 