MATH 152, FALL 2010COMMON EXAM II - VERSION BLAST NAME, First name (print):INSTRUCTOR:SECTION NUMBER:UIN:SEAT NUMBER:DIRECTIONS:1. The use of a calculator, laptop, or computer is prohibited.2. In Part 1 (Problems 1-10), mark the correct choice on your ScanTron using a No. 2pencil. For your own records, also record your choices on your exam , as Scantronswill NOT be returned!3. In Part 2 (Problems 11-15), present your solutions in the space provided. S how allyour work neatly and concisely and clearly indicate your final answer. You will begraded not merely on the final answer, but also on t he quality and correctness o fthe work leading up to it.4. Be sure to write your name, section and version letter of the exam on the ScanTronform.THE AGGIE CODE OF HONOR"An Aggie does not lie, cheat, or steal, or tolerate those who do."Signature:11. The sequence an=15 − e−n(a) converges to15.(b) converges to14.(c) converges to 5.(d) diverges.(e) converges to 0.2. Which statement is true about the integralˆ∞1sin2xx2dx?(a) The integral diverges by oscillation.(b) The integral converges by comparison toˆ∞11x2dx.(c) The integral converges to 0.(d) The integral diverges by comparison toˆ∞11xdx.(e) The integral diverges by comparison toˆ∞112dx.3. The sequence an=(−1)n(2n2+ 2)3n2+ 1(a) converges to23.(b) converges to −23.(c) converges to 2.(d) converges to 0.(e) diverges.24. Which statement is true about the series∞Xn=2nn3− 5?(a) The series is divergent becausenn3− 5>1nand∞Xn=21nis divergent.(b) The series is convergent becausenn3− 5<1n2and∞Xn=21n2is convergent.(c) The series is convergent because limn→∞nn3− 5= 0.(d) The series is convergent because limn→∞nn3−51n2= 1 and∞Xn=21n2is convergent.(e) The series is divergent because limn→∞nn3− 56= 0.5. Which of the fo llowing series is convergent?(a)∞Xn=11n(b)∞Xn=21n ln n(c)∞Xn=113√n(d)∞Xn=11n3/2(e) More than one of these series is convergent.36. Which of the following is the form of the partial fraction decomposition ofx + 3(x + 1)2(x2+ 2x + 3)?(a)Ax + 1+B(x + 1)2+Cx2+ 2x + 3(b)Ax + B(x + 1)2+Cx + 3+Dx − 1(c)Ax + 3+Bx + 1+C(x + 1)2+Dx − 1+Ex + 3(d)Ax + 1+Bx + C(x + 1)2+Dx2+ 2x + 3(e)Ax + 1+B(x + 1)2+Cx + Dx2+ 2x + 37. Computeˆ3−11x2dx.(a)43(b) ln 9(c) −43(d)23(e) The integral diverges8. Which of the following integrals gives the area of the surface obta ined by ro t atingthe curve y = e2x, 0 ≤ x ≤ 1 about the x-axis?(a)ˆ102πx√1 + 4e4xdx(b)ˆ102πxr1 +14e4xdx(c)ˆ102πe2x√1 + 4e4xdx(d)ˆ102π√1 + 2e2xdx(e)ˆ102πe2xr1 +14e4xdx49. The nth part ia l sum of a series∞Xn=1anis given by sn=2n − 1n + 1. Which of thefollowing statements is true?I. The series∞Xn=1anconverges to 2II. The series∞Xn=1andiverges by the Test for DivergenceIII. The sequence anconverges to 0(a) only I and III are true(b) only I is true(c) only II and III are true(d) only II is true(e) all three statements are true10. After an appropriate substitution, the integralˆ2√3√4 − x2dx is equivalent towhich of the following?(a) 4ˆπ/2π/6sec θ tan2θ dθ(b) 4ˆπ/2π/3cos2θ dθ(c) 2ˆπ/2π/3cos θ dθ(d) 4ˆπ/2π/6cos2θ dθ(e) 2ˆπ/2π/6tan θ dθ5PART II WORK OUTDirections: Present your solutions in the space provided. Show all your workneatly and concisely and Box your fi nal answer. You will be graded not merely onthe final answer, but also on the quality and correctness of the work leading up toit.11. (10 points) Computeˆdxx2√x2− 4612. (8 points each) Find the sum of the following series or show they are divergent:(a)∞Xn=02 + 2n10n(b)∞Xn=02(n + 1)(n + 3)713. (6 points each) Given the curve parametrized byx = cos t + t sin t, y = sin t −t cos t, 0 ≤ t ≤π2:(a) Find the length of the curve.(b) SET UP, BUT DO NOT EVALUATE, an integral to find the area of thesurface formed by rotating the curve about the y-axis.814. (1 0 points) Computeˆ3x2− 4x + 11(x − 1)(x2+ 4)dx915. (6 points each) Given the series∞Xn=13n2e−n3:(a) Show using the Integral Test that the series is convergent.(b) According to Matlab, the third partial sum s3≈ 1.107663875. Use the re-mainder theorem t o estimate the largest possible error.10DO NOT WRITE BELOW!QuestionPoints Awarded Points1-10 4011 1012 1613 1214 1015 12TOTAL
View Full Document
Unlocking...