105-Mid2Prac2

# 105-Mid2Prac2 - 9 x 2 4 Evaluate the limit lim x,y →(4 1...

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Math 105 Practice Midterm 2 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. Find the area of the region in the ﬁrst quadrant that is bounded above by y = x and below by the x -axis and the line y = x - 2. 2. A bank account has \$20 , 000 earning 5% interest compounded continuously. A pen- sioner uses the account to pay himself an annuity, drawing continuously at a \$2000 annual rate. How long will it take for the balance in the account to drop to zero? 3. Sketch the xy -trace, xz -trace, and yz -trace of the surface z = 4 y 2 -
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Unformatted text preview: 9 x 2 . 4. Evaluate the limit lim ( x,y ) → (4 , 1) x 2-4 xy 4 √ x-2 y 2 , or show that it doesn’t exist. 5. Consider the function f ( x,y ) = x 2-3 y 2 . (a) Calculate f x and f y . (b) Find the rate of maximum increase when x = 3, y = 2. (c) Sketch the level curve at height z = 4. Find the slope dy dx of the tangent line to this level curve at ( x,y ) = (4 , 2). 6. Find the linear approximation for p (3 . 06) 2 + (3 . 92) 2 . 7. Find the critical points of f ( x,y ) = 3 y 2-2 y 3-3 x 2 + 6 xy , and classify each one as a maximum, minimum or saddle point....
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