(a) Use a graphing calculator to sketch the graph of f (x) = eax sin x, x 0 for a = 0.1

Chapter 3, Problem 21

(choose chapter or problem)

(a) Use a graphing calculator to sketch the graph of f (x) = eax sin x, x 0 for a = 0.1, 0.01, 0, 0.01, and 0.1. (b) Which part of the function f (x) produces the oscillations that you see in the graphs sketched in (a)? (c) Describe in words the effect that the value of a has on the shape of the graph of f (x). (d) Graph f (x) = eax sin x, g(x) = eax , and h(x) = eax together in one coordinate system for (i) a = 0.1 and (ii) a = 0.1. [Use separate coordinate systems for (i) and (ii).] Explain what you see in each case. Show that eax eax sin x eax Use this pair of inequalities to determine the values of a for which lim x f (x) exists, and find the limiting value.