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

Chapter 13, Problem 57

(choose chapter or problem)

Consider the function

\(f(x, y)=\frac{4 x y}{\left(x^{2}+1\right)\left(y^{2}+1\right)}\)

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

(a) Find a set of parametric equations of the normal line and an equation of the tangent plane to the surface at the point (1, 1, 1).

(b) Repeat part (a) for the point \(\left(-1,2,-\frac{4}{5}\right)\).

(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) = 4xy / (x^2 + 1) (y^2 + 1)

-2 leq x leq 2

0 leq y leq 3

(- 1, 2, - 4 / 5)