Calculus 1000A/B Study Guide - Quiz Guide: Polynomial Long Division, Asymptote

• School: Western University
• Department: Calculus
• Course: Calculus 1000A/B
• Professor: Chris Brandl

Document Summary

Assignment 8 solutions: evaluate the following limits. (cid:19) (cid:18) 1 (cid:19) x (a) lim x x x sin. This is of the type 0 so we have an indeterminate product. We will manipulate x sin so that we can apply l"hopital"s rule. (cid:18) 1 (cid:18) 1 (cid:19) x lim x x sin (cid:19) 0 x sin(cid:0) 1 (cid:1) (cid:18) cos(cid:0) 1 (cid:1)(cid:0) 1 (cid:1) (cid:19) (cid:18) 1 x. = 1 (b) lim x x2 ln (x) + ex. This is a limit of the type lim x x2 ln (x) + ex = lim x . So we apply l(cid:48)hopital(cid:48)s rule again (cid:16) This is of the type 1 so we have an indeterminate power. 0 so we apply l"hopital"s rule. lim x 0+ Thus: a closed box is to be constructed so that its base length is three times the base width and is to have a volume of 450 cm3.