MATH 41 Midterm: MATH 41 Stanford finpracA

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

Document Summary

Math 41 fall 2005 practice final exam: evaluate each of the following limits. If there is an in nite limit, then state whether the limit is or (a) lim x (ln x)2 x. 2te t (b) lim t 0 (c) lim x 0+ cos x x: di erentiate each of the following functions (a) y = x(ex) (b) f (y) = ey2 3 sin( y) (c) g(x) = z x2. 2 ecos t+7t2 dt: evaluate each of the following integrals. dx. 1 dt (ln x)2 dx sin x x2 + 2 t (a) z e (b) z 1 (c) z (d) z tan 1 x dx (e) z 2 (f) z 2s2 + s t 1 s3/2 x(x2. 2x x2 + 1 on the interval: a beacon that makes one revolution every 10 s is located on a ship anchored 4 km from a straight shoreline.