MATH 121 Final: MATH 121 Amherst F12M121 2803 29VellemanFinal

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 121
• Professor: All

Document Summary

Dec. 18, 2012: (5 points each) compute the following limits. You should say if the limit is equal to a particular value, if it is , or if it does not exist. (a) lim x 0 xex sin x. 1 cos(3x) (ex 4x)1/x. (b) lim x 0: (8 points each) compute the following integrals. (a) z 2x3 4 x3 2x2 dx. (b) z sin tan2 d . (c) z. X2 + 2x + 5 x dx: (10 points) the curve y = 2 x, 1 x 3, is revolved about the x-axis. Find the area of the resulting surface: (8 points each) for each of the following improper integrals, determine whether the integral converges or diverges. If it converges, nd its value. dx x2 + 3. 1 (a) z (b) z 1 ln x dx. 0: (5 points each) compute the following sums. (a) 5n+1 . (b) 1 ln 7 + (ln 7)2.