MAT 302 Calculus

MAT 302 Assignment Problem 9.3 |Borough of Manhattan Community College9.3 The Integral Test and p-seriesQuestion 1(1 point) Compute the value of the following improper integral. If it converges, enter its value. Enterinfinityif it diverges to∞∞, and-infinityif it diverges to−∞−∞. Otherwise, enterdiverges.Question 2Use the Integral Test to determine whether the infinite series is convergent.∑n=5∞2ne−n2Fill in the corresponding integrand and the va

MAT 302 Assignment Problem 9.2 | Borough of Manhattan Community College9.2 Series and ConvergenceQuestion 1(1 point) Find the numerical value of the sums below.Question 21 point) Find the numerical value of the sum below.Question 3(1 point) Enter a formula forQuestion 4Compute the partial sumsS2,S4S2,S4, andS6S6.Question 5(1 point)Compute the partial sumsS2,S4S2,S4, andS6S6.Question 6(1 point) Ifsn=∑i=1n(12)i,sn=∑i=1n(12)i,then list the first fiv

MAT 302 Assignment Problem 9.1 | Borough of Manhattan Community College9.1 SequencesQuestion 1(1 point) List the first five terms of the sequence:Question 2(1 point) List the first five terms of the sequence:Question 3Calculate the first four terms of the following sequence, starting withn=1n=1.Question 4 Match the graphs with the corresponding formulas Question 5(1 point) Find a formula for the general termananof the seque

MAT 302 Assignment Problem 8.8 |Borough of Manhattan Community College8.8 Improper IntegralsQuestion 1(1 point) Compute the value of the following improper integral. If it is divergent, type "Diverges" or "D".Question 2(1 point) Compute the value of the following improper integral. If it is divergent, type "Diverges" or "D".Question 3(1 point) Match the following improper integral with the improper integral below in which you can compare using th

MAT 302 Assignment Problem 8.5 |Borough of Manhattan Community College8.5 Partial FractionsQuestion 1Question 2(1 point)Which of the following is the correct form of the partial fraction decomposition ofx4 Question 3(1 point)Which of the following is the correct form of the partial fraction decomposition ofx4x4−1?Question 4(1 point)Which of the following is the correct form of the partial fraction decomposition ofQuestion 5(1 point)Which of the

MAT 302 Assignment Problem 8.4 | Borough of Manhattan Community College Question 1(1 point) Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter (A,B,C,D, or E) in each blank. A.tan(sin−1(x/4))tan⁡(sin−1⁡(x/4)) B.cos(sin−1(x/4))cos⁡(sin−1⁡(x/4)) C.(1/2)sin(2sin−1(x/4))(1/2)sin⁡(2sin−1⁡(x/4)) D.sin(tan−1(x/4))sin⁡(tan−1⁡(x/4)) E.cos(tan−1(

MAT 302 Assignment Problem 8.2 | Borough of Manhattan Community College8.2 Integration by partsQuestion 1(1 point)Solve∫(11x+7)exdx∫(11x+7)exdxusing Integration by Parts.Useu=11x+7u=11x+7anddv=exdxdv=exdx.Question 2point) Use integration by parts to find the following:∫(t+7)e2t+3dtQuestion 3(1 point) Use integration by parts to evaluate the integral.Question 4(1 point) Evaluate the indefinite integral. ∫lnxx6dxQuestion 5(1 point) Evaluate the in

MAT 302 Assignment Problem 7.4 |Borough of Manhattan Community College7.4 Arc length and Surface of RevolutionQuestion 1(1 point) Find the arc length of the graph of the functiony=x36+12xy=x36+12xover the interval[1,2]Question 2(1 point) Find the arc length of the graph of the functiony=2x32+3y=2x32+3over the interval[0,9][0,9].Question 3(1 point) Find the arc length of the graph of the functiony=ln(cosx)y=ln(cosx)over the interval[0,π3]Question

MAT 302 Assignment Problem 7.3 |Borough of Manhattan Community CollegeQuestion 1(1 point) The volume of the solid obtained by rotating the region enclosed byy=8x−2x2,y=0y=8x−2x2,y=0about the y-axis can be computed using the method of cylindrical shells via an integralQuestion 2(1 point) The volume of the solid obtained by rotating the region enclosed byy=x2,x=2,x=3,y=0y=x2,x=2,x=3,y=0about the linex=5x=5can be computed using the method of cylindr

MAT 302 Assignment Problem 7.2 | Borough of Manhattan Community College7.2 Volume The Disk MethodQuestion 11 point) The volume of the solid obtained by rotating the region enclosed byy=e5x+4,y=0,x=0,x=0.5y=e5x+4,y=0,x=0,x=0.5about the x-axis can be computed using the method of disks or washers via an integralQuestion 2(1 point) The volume of the solid obtained by rotating the region enclosed byx=0,y=1,x=y2x=0,y=1,x=y2about the liney=1y=1can be co