Chapter 4.3, Problem 63ES

(a) Determine whether the following limits exist, and if so, find them: $\underset{x\to +\infty }{\lim }{e}^x\cos x,\underset{x\to -\infty }{\lim }{e}^x\cos x$

(b) Sketch the graphs of the equations $y=e^x,y=-e^x,$ and $y=e^x\cos x$ in the same coordinate system, and label any points of intersection.

(c) Use a graphing utility to generate some members of the family $y=e^{ax}\cos bx$ ( $a>0$ and $b>0$ ), and discuss the effect of varying a and b on the shape of the curve.