1271practicemidterm3F2009

# 1271practicemidterm3F2009 - Name Signature Section Math...

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Name: Signature: Section: Math 1271. Lecture 030 Practice Midterm Exam III There are a total of 100 points on this 50 minute exam. To get full credit for a problem you must show the details of your work. Answers unsupported by an argument will get little credit. No books, notes, calculators, cell phones or other elecronic devices are allowed. Do all of your calculations on this test paper. Problem Score 1. 2. 3. 4. 5. Total: 1

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Problem 1 Compute the following: a. (5 points) Let F ( x ) = Z x 0 ( K + tan 3 θ ) where K is a constant. Find K if F 0 ( π 4 ) = 2 . b. (5 points) Evaluate the deﬁnite integral Z 1 2 0 dx 1 - x 2 . 2
c. (5 points) Compute f 0 ( x ) if f ( x ) = Z 5 x 2 - 1 1 sin( t 3 ) dt. d. (5 points) Evaluate lim h 0 (1 + 5 h ) 1 h . 3

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Problem 2 (20 points) Find the area of the ﬁnite region in the plane bounded by the curve y = - x 2 + x + 2 and the x -axis. 4
Problem 3 (20 points) Find the absolute maximum and absolute minimum of f ( x ) = x - sin(2 x ) on the interval [0 , π 4 ] . (Some possibly useful facts: π 3 . 14 , 2 1 . 41 , 3 1 . 73 .) 5

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1271practicemidterm3F2009 - Name Signature Section Math...

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