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1 FINAL Eam REVIEW Math 1325 HCCS Name ate MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1 The total cost to hand-produce large dolls and small dolls is given b C(, = If a total of 70 dolls must be made, how should production be allocated so that the total cost is minimized? A Make 35 large dolls and 35 small ones B Make 69 large dolls and 1 small one C Make 70 large dolls and 0 small ones Make 0 large dolls and 70 small ones 2 A compan is manufacturing a new digital watch and can sell all it manufactures. The revenue (in dollars is given b R( = 50-2, where the production output in one da is watches. If 50 production is increasing at 5 watches per da when production is 375 watches per da, find the rate of increase in revenue. A $75 per da B $250 per da C $150 per da $175 per da 3 Suppose the suppl function of a certain item is given b S( = and the demand function is ( = 27-2/3. Find the producer's surplus. A 64 B 64 C If the average cost per unit C( to produce units of plwood is given b C( = 32 the unit cost for units? Round our answer to the nearest cent. A $3.00 B $60.00 C $40.00 $ , what is A certain noise produces watt/m 2 of power. What is the decibel level of this noise (to nearest decibel? Use the formula = log (S/S0, where S0 = -12 watt/m 2. A 68 decibels B 179 decibels C 78 decibels 8 decibels 6 In a lab eperiment 4 grams of acid were produced in 24 minutes and grams in 43 minutes. Let be the grams produced in minutes. Write an equation for grams produced. A 19 = B 19 = 6-68 C = = A force acts on a certain object in such a wa that when the object has moved a distance of r (in m, the force f (in newtons is given b f = 7r 2 + 3r. Find the work (in joules done through the first four meters. A 40 J B J C 64 J J 7 1

2 8 Find the producer's surplus if the suppl function of some item is given b S( = Assume that suppl and demand are in equilibrium at = 30. A 18,900 B 19,800 C 17,200 12, Suppose that the acceleration of an object is given b a(t = 5t 2/3 + 2e -t. The velocit of the object at time 0 is v(0 = 6 and its position at time 0 is s(0 = -5. Find s(t. A 3t 5/3-2e -t + 8 B 9t8/3 8 C 200t8/ e -t + 6t e -t 9t + 4t - 7 8/3 + 2e 8 -t +8t - 7 A cube 4 inches on an edge is given a protective coating 0.3 inches thick. About how much coating should a production manager order for 500 cubes? A About 14,400 in.3 B About 7200 in.2 C About 9600 in.3 About 2400 in.2 11 Newton's law of cooling states that the rate at which a bod changes temperature is proportional to the difference between its temperature and that of the surrounding medium. If a bod is in air of temperature 35 and the bod cools from 95 to 50 in 30 minutes, find the temperature of the bod after 60 minutes. (Round to nearest degree. A 41 B 37 C Find the equation of the line tangent to the graph of f at the indicated value of. 12 f( = 2 + ln 3 ; = e A = 3 e - 2 B = 3 e + 5 C = 3 e 12 = 3 e + 2 Without graphing, describe the shape of the graph of the function and complete the ordered pairs (0, and (1,. 13 f( = 5 - A The graph lies above the -ais, falls from right to left, with the negative -ais as a horizontal asmptote; (0, 5 and 1, B The graph lies above the -ais, falls from left to right, with the negative -ais as a horizontal asmptote; (0, 1 and 1, C The graph lies above the -ais, falls from right to left, with the positive -ais as a horizontal asmptote; (0, 5 and 1, 1 5. The graph lies above the -ais, falls from left to right, with the positive -ais as a horizontal asmptote; (0, 1 and 1, Provide an appropriate response. 14 Find the slope of the secant line joining (2, f(2 and (3, f(3 for f( = A 55 B 15 C

3 15 Find f'( for f( = log6( A C (ln 6( B 54 (ln (ln 6( If a, b, and c are all nonzero, then determine if the plane a + b + cz = 1 alwas intersects all three coordinate planes (i.e. the planes = 0, = 0, z = 0, sometimes intersects them, or never intersects them. A Alwas B Sometimes C Never Let C( be the cost function and R( the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions. C( = ,000 R( = 450 A C'( = R'( = 450 P'( = B C'( = R'( = 450 P'( = C C'( = R'( = 450 P'( = Suppose two automobiles leave from the same point at the same time. If one travels north at 60 miles per hour and the other travels east at 45 miles per hour, how fast will the distance between them be changing after three hours? A 75 mph B 50 mph C 125 mph 150 mph Find d/d b implicit differentiation = 5 19 A d d = B d d = C d d = 2 2 d d = Solve the inequalit and epress the answer in interval notation: > 0. A (-5, B (-5, 0 (4, C (-5, 0 (4, 20 Find the integral p 2 e (4p3 dp A 4 3 e(4p3 + C B 16 9 e(4p3 + C C 16 3 e(4p3 + C 4e (4p3 + C 21 3

4 d A ln + C B ln + C 22 C ln + C ln + C Find the derivative. 23 = ( A d d = 3 4(2-3 ( C d d = 3 5(2-3 ( B d d = 3 4(2-3 ( d d = 3 5(2-3 ( Find the particular solution of the differential equation. 24 d/d - - = 0; = when = 1 A = e -2 B = e C = e-2 = e (2-1/2 Give the equation of the vertical asmptote(s of the rational function. 25 g( = A = -1 B = 1 C = 8 = 1, = Factor completel. 26 z 2-7z - 12 A (z - 3(z + 4 B (2z + 3(5z - 4 C (2z - 3(5z + 4 Prime 26 Find f (. 27 f( = 3 ln + ln 7 + 5e A + 5e B + 5e-1 C e e Convert the temperature C = F A 3.8 F B 95.0 F C F 51.4 F Use a table of integrals to solve the problem. 29 How long will it take for the population of a certain countr to double if its annual growth rate is 3.6%? Round to the nearest ear. A 19 ears B 8 ears C 1 ear 56 ears 29 4

5 Graph the rational function. 30 Pf( = A B - - C - - Find d for the indicated function. d 31 = A 4-8 ln 8 B 4-8 ln 8 C 4-8 ln ln

6 Evaluate the definite integral d 1 A 9 ln 3-1 B ln 3 C ln ln 3 32 ifferentiate. 33 Find f'( for f( = (2-4( A f'( = B f'( = C f'( = f'( = Write the epression as the logarithm of a single number or epression with a coefficient of 1. Assume all variables represent positive numbers ln ( ln ( A ln ( ( B ln ( ( C ln 3( + 9 ( ln 6( + 9 ( Convert to eponential form. 35 log = -6 A -6 = B = 0 C = -6-6 =

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