Calculus 1000A/B Quiz: Assignment 5 Solutions.pdf

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

Document Summary

Assignment 5 solutions: evaluate each of the following limits (a) lim x . 1 + 4 x (cid:113) x2(cid:0)1 + 4x (cid:113) 3ex + e x ex e x+1 = lim x lim x . 3ex + 1 ex ex e ex. 1 (cid:19) x 3e2x = 0 and lim lim x e2x = 0 (c) lim x e x sin x + 2. 4x2 2x + 1 2x = lim x (cid:16) lim x (cid:17)(cid:18) . 4x2 2x + 1 + 2x (cid:19) (cid:1) + 2x. X x < 0 sin (x) x 0. We need to compute f(cid:48)(0) = lim x 0 f (x) f (0) x 0 but since f is de ned di erently on. 2 either side of x = 0 we must observe left and right hand limits. f (x) f (0) x lim x 0 x sin (0) x x x.