MATH 221 Final: MATH 221 KSU f08Final

• School: Kansas State University
• Department: Mathematics
• Course: MATH 221
• Professor: All

Document Summary

The point value of each problem is given in the left-hand margin. Z sec x dx = ln| sec x + tan x| + c , Z csc x dx = ln| csc x + cot x| + c. 2 (cid:18)u a2 u2 + a2 arcsin u a(cid:19) + c , 2 (cid:16)u u2 a2 a2 ln|u + u2 a2|(cid:17) + c. Xn=0 ( 1)nx2n+1 (2n + 1)! cos x = 2n + 1: evaluate the following integrals. (7) a) z ln x x3 dx page 1 of 8 (9) b) z dx (1 + x2) Show all work. (7) a) lim x 0 e3x + e x 2 sin(5x) (7) b) lim x 0 (1 + 3x)1/x (7) 4. Find the taylor series for f (x) = 1/x about a = 2 . (you may use the geometric series formula. ) pg score/29 (10) 5. Solve the initial value problem, 3x dy dx.