MA 312 - Section Number _________ Final Exam Name__________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the integral. (8x2 + x-3 ) dx 1) A) 1) 8x3 x-2 + +C 3 2 C) - B) - 8x 3 x-2 +C 3 2 D) 8x 3 x-2 + +C 3 2 8x3 x-2 +C 3 2 te-7t2 dt 2) A) 2) 1 -7t2 e +C 14 Find the area between the curves. 3) y = x2, y = 4 32 A) 3 B) 1 -7t2 e +C 7 C) - 31 B) 3 1 -7t2 e +C 7 34 C) 3 D) - 1 -7t2 e +C 14 37 D) 3 Use integration by parts to find the integral. Round the answer to two decimal places if necessary. 1 x dx 4) x+1 0 A) -1.33 B) -2.27 C) 0.39 D) -0.94 3) 4) Use the table of integrals or a computer or calculator with symbolic integration capabilities to find the integral. 1 dx 5) 5) x2 - 49 A) 1 x-7 ln +C 14 x+7 C) ln x + B) x2 - 49 + C 1 7+x ln +C 14 7-x D) ln x + x2 + 49 + C Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by the curves. 6) f(x) = 3x + 2 , y = 0, x = 1, x = 5 6) A) 44 B) 44 C) 80 D) 80 Evaluate the improper integral. If the integral does not converge, state that the integral is divergent. 5 7) 1 8x(x + 1)2 A) -0.746 dx 7) B) -5.965 C) 0.625 1 D) 0.120 Find the partial derivative. z . 8) Let z = g(x,y) = 9x + 7x2 y2 - 4y2. Find y A) 14xy2 - 8y 8) B) 9 + 14xy2 C) 14x2y - 8y Find the indicated relative minimum or maximum. 9) Minimum of f(x,y) = x2 - 14x + y2 - 16y, subject to 2x + 3y = 12 A) f(1, 5) = -68 B) f(3, 2) = -61 D) 9 + 14x2 y 9) C) f(2, 0) = -24 Evaluate the iterated integral. 2 5 (9x2 y + 5xy) dy dx 10) 0 0 85 A) B) 85 2 D) f(0, 1) = -15 10) C) 425 2 D) 425 Find the expected value of the probability density function to the nearest hundredth. 1 ; [1, 4] 11) f(x) = 1 x A) 2.83 B) 2.67 C) 3.00 11) D) 2.50 Find all local extreme values of the given function and identify each as a local maximum, local minimum, or saddle point. 12) f(x, y) = 4 - x4 y4 12) A) f(4, 4) = -65,532, local minimum B) f(0, 0) = 4, local maximum; f(4, 4) = -65,532, local minimum C) f(4, 0) = 4, saddle point; f(0, 4) = 4, saddle point D) f(0, 0) = 4, local maximum Evaluate the integral. /12 tan4 3t dt 13) - /12 2 A) 9 9 13) B) - 4 9 C) 6 - 4 9 D) 6 Find the sum of the series as a function of x. (x + 8)n 14) n=1 A) - x+8 x+9 14) B) - x+8 x+7 C) 2 x+8 x+9 D) x+8 x+7 Find the derivative. 15) s = t5 - csc t + 18 ds = 5t4 + csc t cot t A) dt C) ds = t4 - cot2t + 18 B) dt ds = 5t4 - csc t cot t dt D) Find the Taylor series generated by f at x = a. 16) f(x) = x3 - 5x2 + 10x - 10, a = 5 A) (x - 5)3 - 10(x - 5)2 + 15(x - 5) - 40 ds = 5t4 + cot2 t dt B) (x - 5)3 + 10(x - 5)2 + 15(x - 5) + 40 D) (x - 5)3 + 10(x - 5)2 + 35(x - 5) + 40 C) (x - 5)3 - 10(x - 5)2 + 35(x - 5) - 40 3 15) 16)
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