{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

105-Mid2Prac1

# 105-Mid2Prac1 - 1 2 1 4,f 1 2 1 4 on the hill Also ﬁnd a...

This preview shows page 1. Sign up to view the full content.

Math 105 Practice Midterm 1 for Midterm 2 This practice midterm may be harder and/or longer than the real midterm. Not all question will be worth the same number of points. 1. Evaluate Z 0 e - x x dx , or show that it doesn’t exist. 2. Solve the initial value problem y 0 = 1 xy , y (1) = 4. 3. Find an equation for the plane that is parallel to x - 2 y + 6 z = 1 and contains the point (4 , 0 , 2). 4. Sketch the level curves of z = y 2 - 1 4 x 2 at the heights z = - 1 , 0 , 1. 5. Evaluate the limit lim ( x,y ) (0 , 0) 5 x - 2 y 2 x + 2 y 2 , or show that it doesn’t exist. 6. Consider the hill given by the function z = f ( x, y ) = p 1 - x 2 - 4 y 2 . (a) Compute f x and f y . (b) Find the unit vector that gives the direction of steepest ascent at the point
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ( 1 2 , 1 4 ,f ( 1 2 , 1 4 )) on the hill. Also ﬁnd a unit vector that gives the direction of no change at that point. (c) Suppose you’re walking over the hill along the path that is right above the path ( x ( t ) ,y ( t )) = ( t,t 2 ) in the xy-plane. As you pass the point ( 1 2 , 1 4 ,f ( 1 2 , 1 4 )) , at what rate is your height changing? 7. Find the critical points of f ( x,y ) = 1 2 x 2 + 4 xy + y 3 + 8 y 2 + 3 x + 2, and classify each one as a maximum, minimum or saddle point....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online