Radhika Gupta
Math 2210-005, Fall 2014
November 5
Midterm 2
INSTRUCTIONS:
1. Calculators are NOT allowed.
2. REMEMBER : Don’t spend too much time on problems which are worth very few points.
3. Don’t get stuck on a problem, KEEP MOVING ON and in the end come back to the problems you
could not figure out on first try.
4. Show proper work to get full points. If your answer is wrong you still have a chance of getting
partial credit for the work.
Maximum Points
75 points
Number of Pages : 6
Question No.
Marks
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Radhika Gupta
2
Math 22 10-005, Fall 2014
November 5
Chain Rule [10 points]
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st. Find
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Math 2210-005, Fall 2014
November 5
Normal line at a point on a surface [15 points]
A fly sat at the point (1,2,—i) on a grape in the shape of an ellipsoid 8x
2 + 4y
2 + 8z
2 —32 = 0. Assume
the origin is at the center of the grape. The grape was not sweet enough so it decided to fly away. It took
off along the normal line to the grape.
(a) Draw a cartoon of the ellipsoid with the point (1,2, —1) on it and the normal line at (1,2, —1).
(b) What is the equation of the line along which the fly flies off?
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