MAT137Y1 Study Guide - Final Guide: K2K Experiment, Squeeze Theorem, Maxima And Minima
70
MAT137Y1 Full Course Notes
Verified Note
70 documents
Document Summary
Solutions, common errors, and comments: for this question, consider the function g(x) = x42. (a) [2 points] calculate g(cid:48)(1). Comments: for this question only, we accepted solutions without an explanation. 1: compute the following limits e2x2 1. 1 cos x (a) [2 points] lim x 0. Either use l h opital"s rule twice, or use taylor series. (cid:2)e xx42(cid:3) (b) [2 points] lim x . Either use the big theorem, or use l h opital"s rule 42 times. (c) [2 points] lim x sin x x. Comments: as usual, a correct answer with a wrong justi cation or without a justi cation does not receive credit. Getting the right answer by accident is still wrong. Solution: use integration by parts to conclude (cid:90) (cid:90) e. Then evaluate at the endpoints to conclude x4 ln x dx = One way to nd this antiderivative is to use the substitution u = ex. and nish it from there.
