MATH 112 Final: MATH112 Exam 2015 Spring

Homework 4 Name Crin Annck MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers Write the first four elements of the sequence. the question. nn+1 3n-1 1D O 1) 1 1 3 2 3' 2'4'3 3 1 5 C)-1,1,5 2 3'2*4 recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence. 2) a1 = 1, an+1 = 5an 2) A) 5, 6,7,8,9 C) 5,25, 125, 625, 3125 B) 1,6, 11, 16, 21 D) 1,5, 25, 125, 625 Find a formula for the nth term of the sequence. 3) 3) 9, 10, 11, 12, 13 (integers beginning with 9) A) an-n+10 B) an = n + 8 D) an n-9 Find the limit of the sequence if it converges; otherwise indicate divergence 4) an-8+(0.3) A) 83 B) 8 C)9 D) Diverges S) an (-1 5) A) 8 B) 28 C)o D) Diverges 6)an Inin) A) 1 6) B) 0 C) In 3 D) Diverges Assume that the sequence converges and find its limit. 7)a1 .4, an + 1 - 刀 A)5 B)3 C)8 D) 4 Determine whether the nonincreasing sequence converges or diverges. 8) an 8) A) Converges B) Diverges Find the limit of the sequence if it converges; otherwise indicate divergence. 9)an 1.2 9) A) 1 C)e? D) Diverges

D DEPae to four decimel places. 7-3) · 2. logo(13.7) 5. log(1000x)6. log(10.000x) 3, log,(Tx) . . 7L log, 13 15937 72. log; 17 1.5812 r) 1.nia). 4 loge(a) . lo 87,5 16644 SR, lag( )· 11.log(을) . 9.log(100). t2 log(125) . TExercise379-82, 78 kph 400 5234endthe haap of 2. log In Exercises 79-82, tuse a graphing utility and the change-of buse property to graph euch function. 64 12. 79, y = loga x . 14. In 16. log, 7 top 17. log N 6 log N 18. log M- 8 Iog M Practice Plus In Exercises 83-88, ler logé 2 = A and logs 3 C. Write each 쯔m(aln 24 kg(25), 23, logfV expression in termesofAmeg,6 ketn') . 86. log, 8I aC 87. log 27 88. lo 16 In Exercises 89-102, determine whether each equation ts true or false. Where possible, show work to spport your conclusion If the statement is false, make the necessary changets) to prodace a true statemenr 32. log 89. In e= 0 false, lne" 90. In 0-tae 91. IoE4(2x3)-3 log4(2x) . 93, x log 10r = X2 true 95. In(5x) + In l = ln(5x)" 92. In(R&) = 31n(2x) trve 94. Inx 1) In In1 96. In x + In(2x) = ln(3x)" 34. 1 V2536. logz 38. In (x +3 log(x + 3) 97. logx + 3) og(2x) (x +1 39. lo 7(x + 1 log(x + 2) 98. log(x + 2)-log(x-1) false.

be parametric esjuations for a tb) C i v i) C intersects esactly one e ine containing the point -1.3. intersects the xy and ntion voctor to find another esqua ne line with the Korm 17) Let C be the line the ine eontaining the point a) Give parametric ejuastions for c (b) Write an equation for C in on vector to find another equa for the same 18. Let C be the line deterimined by the tt (a) Provide a vector b) Give parametricequations fore c 19. Let C be the line determined by the the points where the line + bt.to t et) eplanes. Ia-0, esplain (a) Provide a vector (b) Write an equation for C in s, determine wbether the the distance between the c. 20. We wish to find the distance from C as shown in the figure that fo dinates of points P and Pa, but we do dinates of point Q (a) Ifyuknew the measure of angle θ llows Wek sect, find the point of intent know th- t.5-3,6+7. weould find the distance from point P to lanes r2()3-,4+3t,5-2 Applications ne. Explain why the vation in Washington State. She tonic wastes in one of the tank tank farm is huge, and she d is leaking. Worse yet, the tank g the tanks would req tank farm, an operation that Instead, Emmy has wells dug the tank farm, to try to trace the earth's surface is conside the bottom of the tank farm the distance is given in f taminated groundwater at (1033, 247,-55). If the w of one of the tanks and i what is the location of th the line does not ow you can distance from point P to line C even if you do ne know the measure of angle θ. line containing use the tech- ization for the 24. P023.5), ds(23.5) 25,Pi-1, 3, 7. d = (2,0,4) the leak? eyuivalent.6. Ptbc 53. lan is climbing Mountl He has made a secon mountain. He does n 27, P3, 1), d= (2 5) 28, p(1.3,-2, 4), d= (4,-1,5, 8) In Exercises 29-34, find an equation of the line containing the Proofs ntaning the given pair of points. Express your answer (a) as a vector p ess your an- rametrization, (b) in terms of parametric equations,and ( n 54. Let Ci and C be line symmetric form. 29. P(O,0,0), Q(4,-1,6) and P2 and Qa poin C2 if and only if P ③P(3,-1,7), Q(5,8,-2)