Power Series Problem: The following are three power series. Each term involves a

Chapter 14, Problem C4

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Power Series Problem: The following are three power series. Each term involves a nonnegative integer power of x. (They are also called Maclaurin series or Taylor series.) a. Evaluate the seventh partial sum of the series for f(0.6) (terms through x6 ). Show that the answer is close to the value of e0.6, where e is the base of natural logarithms. b. Evaluate the fourth partial sum of the series for g(0.6). Show that the answer is close to the value of sin 0.6. Show that the fifth partial sum is even closer to the value of sin 0.6. c. Evaluate the fourth partial sum of the series for h(0.6). Which function on your calculator does h(x) seem to be close to? d. Figure 14-4b shows the graphs of y1a cubic function equal to the second partial sum for g(x)and y2 = sin x. Graph these functions on your grapher. Then add the next three terms of the series for g(x) to the equation for y1. Youll get a 9th-degree function. Plot the two graphs again. Sketch the two graphs, and describe what you observe. Figure 14-4b