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Differential Equations: An Introduction to Modern Methods and Applications
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- a. Use your calculator to approximate 0be0.00001xdx for b=10,50,100and1000. b. Based on your answer to part a, does 0e0.00001xdx appear to be convergent or divergent? c. To what value does the integral actually converge?arrow_forwarda. Use your calculator to approximate 0bex2dx for b=1,5,10and20. b. Based on your answer to part a, does 0ex2dx appear to be convergent or divergent? If convergent, what seems to be its approximate value? c. Explain why this integral should be convergent by comparing ex2withexforx1.arrow_forwardDetermine whether each of the following statements is true or false, and explain why. A differential is a real number.arrow_forward
- Suppose that the distance an aircraft travels along a runway before takeoff is given by D = (5/3)t, where D is measured in meters from the starting point and t is measured in seconds from the time the brakes are released. The aircraft will become airborne when its speed reaches 480 km /h. How long will it take to become airborne, and what distance will it travel in that time?arrow_forward2. Solve the following Infinite Integrals. See if they are Convergent or Divergent. sin x dx Л-2 сos aarrow_forwardFor which values of a does fo00 eax dx converge?arrow_forward
- You have an opportunity to buy a business that will earn $10,000 per year continuously over the next 9 years. If you could earn 7% interest compounded continuously, how much would this business be worth now based on the next 9 years of income? That is, which of the following integrals represents the Present Value of the continuous income stream?arrow_forwardFor problems 4athrough 4d use either integration or the comparison test. Determine whether the following Improper integral converges or diverges. Evaluate if convergent. For c and d ONLY! c) ∫ 1+sinx/xdx d) ∫ dx/x^2-2xarrow_forwardFind the smallest value of the positive constant m that will make mx - 1 + (1/x) greater than or equal to zero for all positive values of x.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,