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MATH 142 Business Math II, Week In Review Spring, 2015, Problem Set 8 (6.1, 6.2, 6.3) JoungDong Kim 1. Find the antiderivative. Z (a) x0.01 dx (b) Z 5 dx (c) Z 1 dy 2y 5 (d) Z y2 √ dy 2 3 1 (e) Z √ 5 (f) Z u3 du (3u2 + 4u3) du Z √ (g) ( 2u0.1 − 0.1u1.1 ) du 2 (h) Z (i) Z (j) Z (k) Z 3 − 6t2 t2 dt √ √ 3 ( t − t5 ) dt 1 π+ x dx t4 + 3 dt t2 3 (l) Z √ (m) Z (n) Z t(t + 1) dt 1 e − x x dx e−x + 1 dx e−x 4 2. Find the cost function for an adhesive tape manufacturer if the marginal cost, in dollars, is given by 150 − 0.01ex , where x is the number of cases of tape produced. Assume that C(0) = 100. 3. Find the cost function for a spark plug manufacturer if the marginal cost, in dollars, is given by 30x − 4ex , where x is the number of thousands of plugs sold. Assume no fixed costs. 5 4. Find the indefinite integral. Z (a) 8(3 − 2x)5 dx (b) Z 10x(2x2 + 1)3 dx (c) Z (x3 + 2)(x4 + 8x + 3) 3 dx 1 6 (d) Z √ 5 (e) Z ln 2x dx x (f) Z e1/x dx x3 x dx 2x2 + 5 2 7 (g) Z e2x − e−2x dx e2x + e−2x (h) Z 1 √ dx x ln x 8 5. Find the revenue function for a hand purse manufacturer if the marginal revenue, in dollars, is 2 given by (1 − x)e2x−x , where x is the number of thousands of purses sold. 6. The population of a certain city for the next several years is increasing at the rate given by 2 P ′(t) = 2000(t + 10)e0.05t +t , where t is time in years measured from the beginning of 1994 when the population was 100,000. Find the population at the end of 1995. 9 √ 7. An object travels with a velocity function given by v = t, where t is measured in hours and v is measured in miles per second. What would be the difference between the upper and lower estimates for the object if we divided the interval [0, 1] into 100 subinterval? 10