MATH 250 Final: MATH 250 Amherst S14M250Final

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 250
• Professor: All

Document Summary

May 7, 2012: this is a closed-book examination. No books, notes, calculators, cell phones, communication devices of any sort, or other aids are permitted: you need not simplify algebraically complicated answers. 3: [20 points] evaluate each of the following limits. Be clear if the limit equals a value, + or , or does not exist. (a) lim x 0 lim x . 1 cos x x2 + x cos(x + sinx) (b) (c) (d) lim x 16. 4 x 16 lim x 1 x2. 3x 4: [25 points] compute each of the following derivatives. Ln t + ln t dt: [30 points] compute each of the following integrals. y x (x + 1)2 (a) z tan ln(y) (b) z e (c) z e x (d) z 1. 1 + e x ex dx: [10 points] give an proof that. 2x + 1 x 2: [10 points] let f (x) =