Cosine Function Series Problem: Consider the function g(x) = cos x. a. Show by equating

Chapter 12, Problem 2

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Cosine Function Series Problem: Consider the function g(x) = cos x. a. Show by equating derivatives that the power series expansion for cos x about x = 0 is P(x) = 1 b. Write the next three terms of the series. c. Write the series using sigma notation. Start the index of summation at n = 0. d. Figure 12-4c shows the graph of the fifth partial sum, S4(x). Plot this graph on your grapher. Then plot y = cos x on the same screen. Sketch both graphs. Figure 12-4c e. Plot the graph of the eighth partial sum,S7(x). For what interval of x-values is theS7(x) graph indistinguishable from that of y = cos x? Sketch the result.f. For what interval of x is the eighth partialsum within 0.0001 unit of cos x?g. Explain why the series for P(x) agrees withthe properties of the cosine function.

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