Math 1B Quiz 8 GSI Theo Johnson Freyd http math berkeley edu theojf 08Summer1B Tuesday 29 July 2008 Name Score 10 You have twenty minutes plus the break to complete the following closed note openchalkboard quiz Partial credit will be awarded for correct work and no points will be given for simply writing down the correct answer Please box your final answers Use the back of the page as necessary 1 5 pts Determine if the following sequence converges or diverges If it converges find the limit If it diverges explain how you know s 1 2n 1 e n cos n 1 n 4 ln1n n 2 We assume the sequence converges and try to compute the limit If it diverges we will presumably fail s s 1 2n 1 e n cos n 1 2n 1 e n cos n lim 1 lim 1 lim n n n n n 4 ln1n 4 ln1n s 2 1 n 1 e n cos n lim 1 lim n n n 4 ln1n s 1 limn e n cos n 2 e 4 limn ln1n r 1 0 2 e 4 0 1 e2 the sequence converges 4 2 0 pts Can you make the currently schedule office hours times What s a time during the week for office hours that you would actually attend Yes and I m there every day 3 5 pts Determine whether the following series converges or diverges Explain how you know X n en n 1 nn 1 Remembering Stirling s formula we use the limit comparison test comparing n en nn 1 with 1 n n en n en nn 1 lim n 2 lim n n n 1 n n P n en P which is finite and positive Thus 1 n does But n 1 converges if and only if n P R 1 n diverges by the p test with p 1 2 i e by the integral test comparing with 1 dx x 2
View Full Document
Unlocking...