Let f(t) = cos(et ), where t is measured in radians. (a) Note that f(t) has a horizontal

Chapter 9, Problem 9.3.7

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Let f(t) = cos(et ), where t is measured in radians. (a) Note that f(t) has a horizontal asymptote as t . Find its equation, and explain why f has this asymptote. (b) Describe the behavior of f as t . Explain why f behaves this way. (c) Find the vertical intercept of f. (d) Let t1 be the least zero of f. Find t1 exactly. [Hint: What is the smallest positive zero of the cosine function?] (e) Find an expression for t2, the least zero of f greater than t1.

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