MATH 222 Study Guide - Midterm Guide: Quotient Rule, Vector Projection, Partial Derivative

• School: McGill University
• Department: Mathematics & Statistics (Sci)
• Course: MATH 222
• Professor: Christa Scholtz

Document Summary

Instructions: this is a 2 hour, closed book/notes examination. To get full marks, you must answer all ve questions. Justify all your answers, unless the question instructs you not to. Solution: the easiest way would have been to say that you saw in class that lim xn you can use the ratio test to show that the series n! = 0 for all values of x, so in particular this is true for x = e. Then the test for divergence implies that the sequence must have limit 0. As a third option, you could have shown that n! 2 e n so lim|an| = 0 by the squeeze theorem (see assignment solutions for more details). But you have another theorem that tells you that if |an| tends to 0, then an must also tend to 0. (b) determine whether the series. Solution: either use l"hopital"s rule to show that (k + 2)! k=0 lim.