Math 31A: Differential and Integral Calculus Name: Homework 2 Due: Friday, October 13 at 8pm PT . Tag your pages for this assignment on Gradescope: If you don't, you'll receive a 1% penalty. (You don't need to submit this page if there's no work on it.) . No credit will be given for answers without accompanying work unless otherwise specified. 1. (/7*10) Compute the following limits or show that the limit does not exist. (a) limx-4 x-4 (b) lim,-7 22-49 (c) limx-7 72-49 (d) lim2-_2 27-32-10 20 + 2 5+3 + 8+ 2 (e) limt-0 314-16+2 (f) limx-2 205-2262 2 202 - 4 (g) lime-to 0 sin? (0) +0 cos2 (0) -40 Here are some limit practice problems! 2. (/10) Compute limn-> f( 3 th ) -f (3 , where f is the function with domain and range R defined by the formula f (a) = 202. 3. Evaluate the following limits. 3ac2 -203 (a) (-/5) limx-706 5x3+2-1 (b) (-15) lim x-too 20 4 - 20 3 + 20 2 - 20+ 1 7ac4 - 20 (c) (-/5) lim, too 204-205 taz - x+1 7ac 4 - 205 Here are some practice problems on limits as x goes to infinity! 4. (/5) Assume that f and g are continuous functions such that f (3) = 4 and g(3) = 2. Compute limx-+3(-2x f (x) + sin(2)g(2))