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. 1) a (8×2 +x-3) dx 1) A) 8×3 3 + x-2 2 + C B) – 8×3 3 + x-2 2 + C C) – 8×3 3 x-2 2 + C D) 8×3 3 x-2 2 + C
2) a te-7t2 dt 2) A) 1 14 e-7t2+ C B) 1 7 e-7t2 + C C) – 1 7 e-7t2+ C D) – 1 14 e-7t2 + C
Find the area between the curves. 3) y= x2, y= 4 3) A) 32 3 B) 31 3 C) 34 3 D) 37 3
Use integration by parts to find the integral. Round the answer to two decimal places if necessary. 4) a1 0 x x+ 1 dx 4) A) -1.33 B) -2.27 C) 0.39 D) -0.94
Use the table of integrals or a computer or calculator with symbolic integration capabilities to find the integral. 5) a 1 x2-49 dx 5) A) 1 14 ln x- 7 x+ 7 + C B) 1 14 ln 7+ x 7- x + C C) ln x + x2 – 49 + C 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) 44Δ B) 44 C) 80 D) 80Δ
Evaluate the improper integral. If the integral does not converge, state that the integral is divergent. 7) aQ 1 5 8x(x+ 1)2 dx 7) A) -0.746 B) -5.965 C) 0.625 D) 0.120
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Find the partial derivative. 8) Let z = g(x,y) =9x+ 7x2y2- 4y2. Find ^z ^y
. 8) A) 14xy2 – 8y B) 9+ 14xy2 C) 14x2y- 8y D) 9+ 14x2y
Find the indicated relative minimum or maximum. 9) Minimum of f(x,y)= x2 – 14x+ y2 – 16y, subject to 2x+ 3y= 12
9)
A) f(1, 5)=-68 B) f(3, 2)=-61 C) f(2, 0)=-24 D) f(0, 1)=-15
Evaluate the iterated integral. 10) aa 2 0 5 0 (9x2y+ 5xy) dy dx 10) A) 85 2 B) 85 C) 425 2 D) 425
Find the expected value of the probability density function to the nearest hundredth. 11) f(x)= 1- 1 x ; [1, 4] 11) A) 2.83 B) 2.67 C) 3.00 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- x4y4 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. 13) aΔ/12 -Δ/12 tan4 3t dt 13) A) Δ 9 – 2 9 B) – 4 9 C) Δ 6 – 4 9 D) Δ 6
Find the sum of the series as a function of x. 14) _ Q n=1 (x+ 8)n 14) A) – x+ 8 x+ 9 B) – x+ 8 x+ 7 C) x + 8 x + 9 D) x + 8 x + 7
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Find the derivative. 15) s =t5- csc t + 18 15) A) ds dt =5t4 + csc t cot t B) ds dt =t4 -cot2t+ 18 C) ds dt =5t4 – csc t cot t D) ds dt =5t4 +cot2t
Find the Taylor series generated by f at x = a. 16) f(x)=x3- 5×2 + 10x- 10, a=5 16) A) (x- 5)3 – 10(x- 5)2+ 15(x- 5) – 40 B) (x- 5)3 + 10(x- 5)2+ 15(x- 5) + 40 C) (x- 5)3 – 10(x- 5)2+ 35(x- 5) – 40 D) (x- 5)3 + 10(x- 5)2+ 35(x- 5) + 40
