21A-FQ03 - First letter of your last name Name Student Id...

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Unformatted text preview: First letter of your last name: Name: Student Id number: MATH 21A. Final Exam. The exam is “closed book, closed notes, no calculators”. Show all the work: Correct answer without proper justification can result in a very low score on the problem. Scores: 6 7 8 9 10 1 2 3 4 5 Total: 1. (10 points) If lim x → c f ( x ) = A and lim x → c g ( x ) = B , prove, using the definition of the limit, that lim x → c ( f ( x ) + g ( x )) = A + B . 2 2. (10 points) State and prove the theorem about functions with zero deriva- tive on an interval. 3 3. (10 points) You have a cylindrical tank of the radius 5 ft and you are pumping a liquid into this tank at the rate of 0 . 1 cubic ft per minute. Find at which rate the level of the liquid is increasing. (Your answer will involve the number π .) 4 4. (10 points) Compute the limit lim x → 2 x 2- 4 ln( x- 1) 5 5. (10 points, each item is worth 2 points) Mark the true and false statements among the following by writing the word “true” next to the true statements and...
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21A-FQ03 - First letter of your last name Name Student Id...

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