MATH 321 Winter 2014 Midterm Exam Solutions

MATH 321 Winter 2014 Midterm Exam Solutions - Midterm...

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Mathematics 321 Midterm — February 26 th 2014 Page 1 of 5 This midterm has 4 questions on 5 pages , for a total of 100 points. Duration: 50 minutes Read all the questions carefully before starting to work. Continue on the back of the previous page if you run out of space. This is a closed-book examination. None of the following are allowed : documents, cheat sheets or electronic devices of any kind (including calculators, cell phones, etc.) You may use any fact that we proved in class or that was a part of your homework. If you do, you must precisely state the fact that you are using. Full Name (including all middle names): Student-No: Signature: Question: 1 2 3 4 Total Points: 25 25 25 25 100 Score:
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Mathematics 321 Midterm — February 26 th 2014 Page 2 of 5 1. 25 marks Let f : [0 , ) R be a continuous function such that lim x →∞ f ( x ) = L ( −∞ , ). Find the value of lim n →∞ 2 0 f ( nx ) dx , and prove your statement.
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