This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full Document
 Spring '08
 Vershynin
 Calculus, Topology, Derivative, Continuous function

Click to edit the document details