MATH 2300 Exam 1 (Fall 2006)

MATH 2300 Exam 1 (Fall 2006) - MATH 2300: CALCULUS 2...

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Unformatted text preview: MATH 2300: CALCULUS 2 September 20, 2006 MIDTERM 1 I have neither given nor received aid on this exam. Name: 001 J. Newhall ........... (9am) 002 S. Preston ...........(10am) 003 K. Kearnes .......... (11am) 004 S. Preston ...........(12pm) 005 J. Wiscons ............ (2pm) If you have a question raise your hand and remain seated. In order to receive full credit your answer must be complete , legible and correct . Show all of your work, and give adequate explanations. Some useful formulas: Z √ u 2 + 1 du = u 2 √ u 2 + 1 + 1 2 ln ( u + √ u 2 + 1 ) + C Z √ u 2- 1 du = u 2 √ u 2- 1- 1 2 ln ( u + √ u 2- 1 ) + C DO NOT WRITE IN THIS BOX! Problem Points Score 1 30 pts 2 30 pts 3 30 pts 4 30 pts 5 30 pts 6 30 pts 7 30 pts 8 30 pts TOTAL 240 pts 1. (30 points) If Z 1 f ( x ) dx = 12, then what is Z 1 xf ( x 2 ) dx ? If u = x 2 , then du = 2 x dx , so Z 1 xf ( x 2 ) dx = 1 2 Z 1 f ( x 2 ) 2 x dx = 1 2 Z 1 f ( u ) du = 1 2 (12) = 6 . 2. (30 points) Starting with the integral definition of the logarithm function, which is (i) ln( x ) = Z x 1...
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This note was uploaded on 02/28/2008 for the course MATH 2300 taught by Professor Frugoni,er during the Spring '08 term at Colorado.

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MATH 2300 Exam 1 (Fall 2006) - MATH 2300: CALCULUS 2...

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