MATH 41 Midterm: MATH 41 Stanford 12Exam1sol

• School: Stanford University
• Department: MATH - Mathematics
• Course: MATH 41
• Professor: All

Document Summary

Solutions to math 41 first exam october 18, 2012: (12 points) find each of the following limits, with justi cation. If the limit does not exist, explain why. If there is an in nite limit, then explain whether it is or . (a) lim. 1 x 1 (cid:18) 2 x2 1 x 1(cid:19) (4 points) 1 x 1 lim x 1(cid:18) 2 x2 1 . 2 (x 1) (x + 1)(x 1) X + 1 (x + 1)(x 1) (x 1) (x + 1)(x 1) 1 x + 1 (b) lim x ln(2 + x) x2 + 2x + 2 x 2+ (4 points) we have to compute x ln(2 + x) x2 + 2x + 2 lim x 2+ We know that limx 2+ ln(2 + x) = since limx 0+ ln(x) = . So as x goes to 2 from the right, ln(x + 2) becomes a very large negative number.