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Unformatted text preview: Math 1271, Lec 020: Calculus I Fall 2010 Midterm Exam III Instructions Check that this booklet consists of 8 pages including the front page. To get full credit, you must show all steps in your solutions. Calculators are NOT allowed. You don't need to simplify your answer. Good luck! Section and TA: Student ID: Name: Signature: Problems P 1 P 2 P 3 P 4 P 5 P 6 Total Scores
1 1 Problem 1. [14 points] Find the point on the curve y = 2 x2 that is closest to the point (4, 1). 2 Problem 2. [14 points] Find the derivative of the following function.
2+cos x g(x) =
2 et dt 2 3 Problem 3. [12 points] The curve y = f (x) passes through (1, 5) and the slope of the tangent line to this curve at (x, f (x)) is equal to 3x2  4. What is f (2)? 4 Problem 4. [12 points] Evaluate the following limit. 1 n n lim
n 1+
i=1 i n 4 5 Problem 5. [16 points] Find the general indefinite integral. (a) [8 points] 4 1 + x2 + 1  x2 dx (b) [8 points] sec2 x tan3 xdx 6 Problem 6. [32 points] Find the definite integral.
3 (a) [8 points]
0 x2  4dx e (b) [8 points]
1 (ln x)3 dx x 7 2 (c) [8 points]
0 x dx x4 + 1 3 (d) [8 points]
2 2x(x2  3)5 dx 8 ...
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This note was uploaded on 02/07/2012 for the course MATH 1271 taught by Professor Ming during the Fall '08 term at Minnesota.
 Fall '08
 MING
 Calculus

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