MATH 111 Midterm: MATH 111 Amherst F14M111 2801 29Benedetto

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 111
• Professor: All

Document Summary

You have 3 hours to take the nal. No calculators, notes, books, cell phones, communication devices or aids of any sort are allowed. Show all your work and justify all your answers. There are 14 problems on this nal, totalling 350 points. However, numerical expressions such as ln(e2), cos(2 /3), 7 1, and 1/ tan( /6) should be simpli ed completely. *if you nish in the last 20 minutes, please remain seated, so as not to disrupt those who are nishing. If you nish earlier than that, you may drop o your nal at my o ce. Justify completely. (a) (10 pts) lim x 2 (x + 2)2|x 2| x2 4 (b) (10 pts) lim x 2 (x + 2)2|x 2| x2 4. X x 9 lim x 9 (d) (10 pts) lim x ln x + ln(1 + 4x) ln(3x2 + 5) (hint: rewrite: (20 pts) Prove, using the de nition of a limit, that x.