MATH 113 Final: MATH 113 BYU FinalF2005
Document Summary
Do not show your work for problem 1 through 9: please write neatly, notes, books, and calculators are not allowed, expressions such as ln(1), e0, sin( /2), etc. must be simpli ed for full credit. Part i: short answer and multiple choice questions. Do not show your work for problems in this part: fill in the blanks with the correct answer. 1 n(cid:19)n(cid:27) as n if it is convergent, otherwise write divergent. (j) state the integration by parts formula: (k) give a limit de nition of the improper integral z 1. X dx (l) let state the (2n)-th term of the maclaurin series for sin x x. 1 (m) the integral z cot x dx equals: true/false: write t if statement always holds, f otherwise. Let p an = p n=1 an be an arbitrary series. (a) (b) (c) If {an} is a positive decreasing sequence then p( 1)nan converges. If p an converges then an 0.
