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A: SOLUTION-
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Q: In Exercises 47-76, determine convergence or divergence using anymethod covered so far.
A: Given: ∑n=1∞sin1n
Q: Q: Use the Squeeze theorem to estabich cennergence of the gi , ren Sequence Conr Inx X(X+2)
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Q: (b) Check the convergence of the improper integral z1z dr. Z+2
A: Topic- improper integration
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Q: 1. Use the definition of the definite integral as the limit of a Riemann sum to evaluate
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Q: Compute the definite integral as the limit of Riemann sums, Verify by FTC, and using Desmos. 1) y =…
A: By Reimann sum, ∆x=b-an=4-0n=4n Again, xi=0+i·∆x=4in Now,…
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Q: Compute the definite integral as the limit of Riemann sums, Verify by FTC, and using Desmos. 19) y =…
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Q: e the Integral Test to determine the convergence or divergence of Σ n = 0\ е
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A: Solve the following
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Q: 3. Use the integral test to determine if ) 1 is convergent or divergent. Explain n(In (n))* and…
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Q: 1 Use the Cauchy's integral test to show that Σ diverges n. In n. In In n n=2
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Q: The integral in this exercise converges. Evaluate the integral without using tables 00 -1 20 tan…
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Q: 1. x(n) = n(-1)²u(n)
A: Given clear step by step explanation
Q: 2. Determine the convergence of the improper integral e² In x dx.
A: Take the integral, ∫0∞xlnx=lnxx22-∫0∞1x.x22dx=x2lnx2-x240∞=∞ As after taking x→∞ the limit of the…
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A: The answer is found in step-2
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A: according to the integral test the function should be continuous,positive and decreasing function.
Q: Use an appropriate Riemann sum to evaluate the limit
A: Solution:- We have to use an appropriate Riemann sum to evaluate the limit…
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Q: Determine the convergence of the integral tan x J, (In(cos r))² dx. UTM UTN
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Q: 8. Use the integral test to determine if IM8 k² (k³ + 2)3/2 converges.
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Q: Use the Integral Test to determine whether the seriesconverge or diverge. Be sure to check that the…
A: Given series is, Draw the curve of given expression,
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Q: 3n (d) E Vn² – 1 n=2
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Q: a) Prove that the series f(2) = Ee -" sin(nz) n=1 defines a holomorphic function in the strip -1 <…
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- A researcher has investigated the hypotheses H0: u = 10 versus H1: u >10. The researcher has obtained a random sample of 15 elements and based on this sample the researcher does not accept u > 10. Unbeknownst to the researcher u > 10 is true. The researcher has made aThe events are approximately independent because 0.700 = 0.700. The events are not independent because 0.700 = 0.700. The events are approximately independent because 0.731 ≠ 0.700. The events are not independent because 0.731 ≠ 0.700.Q2. Prove that P(A^') = 1 − P(A), for any event A
- The P(A)=0.32P(A)=0.32 and the P(B)=0.09P(B)=0.09. Events AA and BB are mutually exclusive.What is the P(A and B)P(A and B).What are the lower bound and upper bound of the given problem 1c? Is it 0 or 1? P(x is 40 or fewer senior) = binomcdf (n=50, p=0.72, LB=?, UB=?) = 0.9260A city uses three pumps to carry water from a river to a reservoir. Pumps A and B are new, and have a probability of failing of 0.015 on any day. Pump C is older, and has a probability of failure of 0.08 on any day. Pumps A and B operate Monday-Friday. On Saturday, pumps A and C operate while pump B is serviced. On Sunday, pumps B and C operate while pump A is serviced. Answer the following questions, assuming that the pumps operate independently of one another, and independently from day to day. Determine the probability that pump A works on a day that it is in use. Find the probability that pumps A and B both fail on a day they are both in use. Compute the probability that at least one pump fails on any Sunday. Find the probability that pump A works, and C fails on any Saturday. Determine the probability that no pumps fail in a week.
- 1. An experiment consists of asking 3 women at random if they wash their dishes with brandX detergent.Define an event that has its elements the points {YYY, NYY, YYN, NYN}.If P (Event A)=0.2 and P(Event B)=0.3, and the two events are disjoint, then P (Event A and Event B) is?Within the interval (0,1)we randomly choose two numbers: x and y . Determine the probability that the number (5x+y) is divisible by 3 .
- A pharmaceutical company has developed a new drug to help relieve acid reflux. However, as with all new drugs, there are concerns about adverse side effects. To check this, the company administers the drug to n randomly chosen people with acid reflux, and it finds that k of them experience adverse side effects. The company hopes to reject the null hypothesis that the proportion of drug-takers who experience adverse side effects is at least 0.5%. Which of the following is true? a. If n=1,250 and k=1, this is enough evidence to reject the null at the 1% level. b. If n=1,000 and k=3, this is enough evidence to reject the null at the 10% level. c. If n=4,000 and k=9, this is enough evidence to reject the null at the 1% level. d. If n=1,600 and k=4, this is enough evidence to reject the null at the 5% level.6. A smoke detector system uses two devices, an ionization sensor and a photoelectric sensor. If smoke is present, the probability that it will be detected by the ionization sensor (I) is 0.90, by the photoelectric sensor (P), 0.80, and by both devices, 0.72. a) Draw a Venn diagram to represent the problem. b) If smoke is present, determine the probability that the smoke will be detected by the system. c) if smoke is present, determine the probability that the smoke is undetected. d) are the two alarms operating independently. Justify your answer with a calculation.52. Consider two securities, the first having μ1 = 1 and σ1 = 0.1, and the secondhaving μ2 = 0.8 and σ2 = 0.12. Suppose that they are negatively correlated,with ρ = −0.8.a. If you could only invest in one security, which one would you choose, andwhy?b. Suppose you invest 50% of your money in each of the two. What is yourexpected return and what is your risk?c. If you invest 80% of your money in security 1 and 20% in security 2, whatis your expected return and your risk?d. Denote the expected return and its standard deviation as functions of π byμ(π ) and σ (π ). The pair (μ(π ), σ (π )) trace out a curve in the plane as πvaries from 0 to 1. Plot this curve.e. Repeat b–d if the correlation is ρ = 0.1