Solution: Investigation Consider the function on the intervals and (a) Find a set of

Chapter 13, Problem 58

(choose chapter or problem)

Consider the function

\(f(x, y)=\frac{\sin y}{x}\)

on the intervals \(-3 \leq x \leq 3\) and \(0 \leq y \leq 2 \pi\).

(a) Find a set of parametric equations of the normal line and an equation of the tangent plane to the surface at the point \(\left(2, \frac{\pi}{2}, \frac{1}{2}\right)\).

(b) Repeat part (a) for the point \(\left(-\frac{2}{3}, \frac{3 \pi}{2}, \frac{3}{2}\right)\).

(c) Use a computer algebra system to graph the surface, the normal lines, and the tangent planes found in parts (a) and (b).

Text Transcription:

f(x, y) = sin y / x

-3 leq x leq 3

0 leq y leq 2 pi

(2, pi / 2, 1 / 2)

(-2 / 3, 3 pi / 2, 3 / 2)