Chapter 1, Problem 45RE

(a) Sketch the curves $y=\pm e^{-x/2}$ and $y=e^{-x/2}\sin 2x$ for $-\pi /2\le x\le 3\pi /2$ in the same coordinate system, and check your work using a graphing utility.

(b) Find all x-intercepts of the curve $y=e^{-x/2}\sin 2x$ in the stated interval, and find x-coordinates of all points where this curve intersects the curves $y=\pm e^{-x/2}$ .