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midterm2-solutions

midterm2-solutions - MATH 31B SECTION 2 SECOND MIDTERM...

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MATH 31B SECTION 2 SECOND MIDTERM Please note: Show your work. Correct answers not accompanied by sufficent explanations will receive little or no credit. Please call one of the proctors if you have any questions about a problem. No calculators, computers, PDAs, cell phones, or other devices will be permitted. If you have a question about the grading or believe that a problem has been graded incorrectly, you must bring it to the attention of the professor within 2 weeks of the exam. #1 #2 #3 #4 #5 Total SID: TA: Section(circle): Tuesday Thursday Name: 1
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MATH 31B SECTION 2 SECOND MIDTERM 2 Problem 1. Evaluate the definite integral π 2 0 sin 2 x cos 2 x dx Solution. Using sin 2 x 1 2 1 cos2 x and cos 2 x 1 2 1 cos2 x , we get sin 2 x cos 2 x 1 4 1 cos2 x 1 cos2 x 1 4 1 cos 2 2 x 1 4 sin 2 2 x 1 8 1 cos4 x Hence the integral is the same as π 2 0 1 8 1 cos4 x dx π 16
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MATH 31B SECTION 2 SECOND MIDTERM 3 Problem 2. Find the limit lim t 0 t ln sin t Solution. Applying L’Hopital’s rule, we have lim t 0 t ln sin t lim t 0 lnsin
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