NAME: PRINT SOLUTIONS
Calculus IV [2443002] Quiz I
Q1]... Which one of the four functions listed below has the following level curves?
1. 2. 3. 4.
f (x, y ) = (x + 1)(y 2). g (x, y ) = (x 1)(y + 2). h(x, y ) = (x + 1)2 (y 2)2 . k (x, y ) = (x 1)2 (y + 2)2 .
NO Level curves are hyperbolae with asymptotes parallel to the axes, and centered on (1, 2). NO Level curves are hyperbolae with asymptotes parallel to the axes, and centered on (1, 2). NO Level curves are hyperbolae with asymptotes parallel to y = x, and centered on (1, 2). YES curves Level are hyperbolae with asymptotes parallel to y = x, and centered on (1, 2).
Q2]... Compute the rst and second order partial derivatives for the function f (x, y ) = cos(xy ) . Answer: There are two rst order partial derivatives and four second order partial derivatives. The mixed second order partial derivatives are equal by Clairauts Theorem, so we get a total of ve answers. fx (x, y ) = y sin(xy ) fy (x, y ) = x sin(xy ) fxx (x, y ) = y 2 cos(xy ) fxy (x, y ) = fyx (x, y ) = sin(xy ) xy cos(xy ) fyy (x, y ) = x2 cos(xy )