MATH 171 Midterm: Math 171 TAMU Fall 02 Exam3Solutions
Document Summary
December 3, 2002: (5) de ne r b a f (x) dx. sequence of riemann sums. The de nite integral of a function over the interval [a, b] is de ned to be the limit of a. Z b a f (x) dx = lim n n. Xi = 1 f ( i) xi, where xi denotes the length of the ith subinterval and the i is any point in that ith subin- terval. We also assume that the lengths of the subintervals go to zero as n goes to in nity: (30) compute the following: d dx(cid:0)esin 2x(cid:1) = 2 (cos 2x) esin 2x. 1 sin x x + cos x (ln (x + cos x)) = d dx ex d dx(cid:0)sin 1 (ex)(cid:1) = p(1 e2x) Thus, the ratio goes to zero. (a) (b) (c) (d) r (e) (f) 1/x (1/2) x 1/2 = lim x .
