C1T3V2Summer09Solutionspdf

C1T3V2Summer09Solutionspdf - MA 141 Test 3 - Version 2 No...

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Unformatted text preview: MA 141 Test 3 - Version 2 No Work = No Credit! 1. (10 points) Find the linearization L(x) of f(x) = J; at a = 64 and use it to estimate f(63). 2. (12 points) Acid is mixed into a cylindrical tank with a diameter of 8 feet at a rate of 12 ftS/min. Find the rate at which the acid leaves the tank when the level of the acid in the tank is rising at a 1 . . rate of 2— ft/min. Include units with your answer. Hint: Volume of a Cylinder = 7rr2h 7r 3. (20 points) Use f(x) : 2x3 — 3x2 —12x— 2 to answer the following questions: a. State the domain of f(x). b. Find all critical numbers of f(x). c. Find the intervals where f(x) is increasing or decreasing. d. State the x— values of all maximums or minimums of f(x). Clearly label your answers. e. Find the intervals where f(x) is concave upwards or downwards. f. State all inflection points. 4. (8 points) Find the absolute maximum and minimum of the same function. f(x) = 2x3 — 3x2 — 12x — 2. on the closed interval [-2.0]. 5. (23 points) Find the following limits. Verify L’Hospital’s Rule applies before using it. . 5—5005): a. 11m— 7; sinx .\'-—>— 2 2e‘—x2—2x—2 3 l c. lim (1+ mi x—>O 6. (15 points) $480 are available to fence in a rectangular garden. One side of the garden borders a river. here the fencing costs $6/ft, on the other three sides it costs $2/ft. Find the dimensions of the largest possible garden. Verify that this is indeed a maximum using the Second Derivative Tesl 1 . 7. (12 points) Find the most general antiderivative of f(x) = ZSecxtanx +— + 4% + e“ — 7 X b. lim x—>O x Wm \H\ 7—8er 3 Vgswfl Q SQLJRMS \. L54): 5; l(sq Cx—&\ «- 9(a} 4: \ 9 :1C—2>>o \n'éyemca (0) Ac: Agave—0&1? / \ 9 ‘ C53 70 \ (\QVQOO C209\ / locd WHO {:2 Eu {3 P‘CO) 40 E— Am {NOD >0 CC “9 A b X (1 20 ‘2 x) = )2 O x ‘2 K2 At _ 129 “L [X X W23 — C3 l2 0 ‘(DO :6 Q .7 3/ ...
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C1T3V2Summer09Solutionspdf - MA 141 Test 3 - Version 2 No...

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