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Question 1. Use the integral comparison test to determine if the integral oo -22 / sm(7r:1:)d$ 1 333/2 converges or diverges. Hint: use an integral ptest with p = 3/2. Using dcsmos (or your favorite computer graphing tooliNO HAND DRAWN PLOTS WILL BE ACCEPTED) plot the graphs of x) = sin2(27r:t)/:.123/2 and 9(27) = 1/233/2 on the same axis. Restrict your scaxis to the interval 0 S a: S 10 and y-axis to the interval 0 S y S 2. Does your graph support your conclusion from the comparison test? Question 2. Use the graph to answer the following questions You may assume that the trends (end behaviors) in the graphs continue beyond the plotted domain as I > oo. (a) Assume that If\" f(:c)d:r: converges. What can you conclude about floog(:v)d$? What can you conclude about f1 Mm) dat? Explain your answers. (b) Assume {that flm f (:17) dz: diverges. What can you conclude about I100 g(:t:) dm? What can you conclude about f1 h(z) daz? Explain your answers. Question 3. Use the midpoint method and trapezoidal method to estimate the definite integral - x2 dx with N = 5 subintervals.Question 4. Calculate the maximum possible error for estimating the integral 10 f 272 d2: 0 with N = 5 subintervals with both the midpoint and trapezoidal method. Based on your answers from Question 3, what are the actual errors from each estimate? Question 5. Suppose the improper integral of a known function f(x) for x > 1 is known to converge. That is, the integral converges, but we do not know the limiting value of the integral (or it is difficult to compute by hand). Such instances often arise using the integral comparison theorem (Question 1, for example). Our alternative to computing integrals by hand is to use numerical techniques (like the midpoint or trapezoidal method) to approximate definite integrals. What challenges would you expect to face when applying a numerical technique towards a convergent improper integral