Raabe's (or Gauss's) Test The following test, which we statewithout proof, is an extension of the Ratio Test.Raabe's Test: If E,-1u, is a series of positive constants andthere exist constants C, K, and N such thatUnf(n)Un+1n?where | f(n)| < K for n > N, then E=1 u, converges if C > 1and diverges if C < 1.Show that the results of Raabe's Test agree with what youknow about the series E1(1/n²) and E„-1(1/n).

Answered: Image /qna-images/answer/08557fb4-9d22-477c-9a2c-063944b18656.jpg

Answered: Raabe's (or Gauss's) Test The following…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.7: Solving Inequalities

Problem 85E

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Areas of Curved Regions The Monte Carlo method can be used to estimate the area under the graph of a function. The figure below shows the region under the graph of f(x)=x2, above the x-axis, between x=0 and x=1. If we choose a point in the square at random, the probability that it lies under the graph of f(x)=x2 is the area under the graph divided by the area of the square. So if we randomly select a large number of point in the square, we have numberofhitsunderthegraphnumberofhitsinthesquareareaundergraphareaofsquare Modify the program from Problem 5 to carry out this Monte Carlo simulation and approximate the required area.
Salary A teacher makes $32,000 in his first year at Lakeside School and gets a 5% raise each year. (a) Find a formula for his salary Anin hisnth year at this school. (b) List his salaries for his first 8 at this school.
Areas of Curved Regions the Monte Carlo method can be used to estimate the area under the graph of a function. The figure below shows the region under the graph of f(x)=x2 above the x-axis, between x=0 and x=1. if we choose a point in the square at random, probability that it lies under the graph of f(x)=x2 is the area under the graph divided by the area of the square. So if randomly select a large of points in the square, we have Modify the program from Problem 5 to carry out this Monte Carlo simulation and mate the required area.
A Precocious Child and Her Blocks A child has 64 blocks that are 1-inch cubes. She wants to arrange the blocks into a solid rectangle h blocks long and w blocks wide. There is a relationship between h and w that is determined by the restriction that all 64 blocks must go into the rectangle. A rectangle h blocks long and w blocks wide uses a total of h X w blocks. Thus, hw = 64. Applying some elementary algebra, we get the relationship that we need: w=64h(2.3) Use a formula to express the perimeter P in terms of h and w. Using Equation 2.3, find a formula that expresses the perimeter P in terms of the height only. How should the child arrange the blocks if she wants the perimeter to be the smallest possible? Do parts b and c again, this time assuming that the child has 60 blocks rather than 64 blocks. In this situation, the relationship between h and w is w = 60/h. Note: Be careful when you do part c. The child will not cut the blocks into pieces
Home Equity When you purchase a home by securing a mortgage, the total paid toward the principle is your equity in the home. If your mortgage is for P dollars, and if the term of the mortgage is t months, then your equity E in dollars, after k monthly payments is given by E=P(1+r)k1(1+r)t1 Here r is the monthly interest rate as a decimal, with r=APR/12 Suppose you have a mortgage of 425,000 at an APR of 9% and a term of 30 years. How long does it take for your equity to reach half of the amount of the original mortgage? Round r to four decimal places.

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