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6. We want to use the Integral Test to show that the positive series a converges....
an converges. 6. We want to use the Integral Test to show that the positive series All of the following need to be done except one. Which is the one we don't need to n=1 do? (a) Find a function f(x) defined on [1,00) such that f(x) > 0, f(x) is decreasing, and f(n) = an for all n. (b) Show that ſi f(x) de converges. (C) Show that lim f(x) dx exists. t-00 (d) Show that lim sn exists....
(3) Suppose we want to use the integral test to determine if the series k ek converges or diverges, where ak = f (). What conditions must f (x) satisfy in order to justify the use of the integral test? (4) Consider the series relitz (a) Use the integral test to show the above series converges. (b) Use the integral test to fill in the blanks: ----- Et=11th ----
Use the Integral Test to determine if the series converges or diverges. Be sure to check that the conditions of the Integral Test are satisfied. Inn R=3 n
To test the series e 2n for convergence, you can use the Integral Test. (This is also a geometric series, so we could n=1 also investigate convergence using other methods.) Find the value of e-24 dx = Preview Ji What does this value tell you about the convergence of the series e-2n? the series definitely diverges the series might converge or diverge: we need more information the series definitely converges Compute the value of the following improper integral, if it...
00 1 for convergence. It turns out that a good 7. Suppose that we want to test n(In n) test to use is the Integral Test. So, let f(x) n=2 1 Therefore, we want to consider X(In x)2" Z 1 1 dx = lim t00 dx. The next best step is which of the following? x(In x)2 x(In x) (a) Use l'Hospital's Rule. (b) Find the derivative of x(In x)2. (c) Let u = ln x. (d) Let u =...
1. Use the integral to find if the series converges: [~__ ( 2 ) Use the direct comparison test to find if the series converges. Remember to state which series you are using for the comparison. 2. LX-1 (5810)
Prob. 6 (a) (10 points) Use the Integral Test to determine whether the series is convergent or divergent. n(Inn) n2 (b) (10 points) Determine if the series converges or diverges. Mention which test you used. M8 n
Use the pull down menu to state whether the series converges or diverges and by which convergence test. 3m 4 (1y Vn+3 8" n! g0- 32 443 (-1'n Σ 4n+4 00 Σ (+: 4 4 n7 n15 W Converges-Integral/Comparison Test Converges-Ratio Test Converges-Alternating Series Test Diverges-Integral/Comparison Test Diverges-Ratio Test Diverges-Alternating Series Test Use the pull down menu to state whether the series converges or diverges and by which convergence test. 3m 4 (1y Vn+3 8" n! g0- 32 443 (-1'n...
Prev Up Next (1 pt) Use the Integral Test to determine whether the infinite series is convergent. 7 Inn n2 n=2 Fill in the corresponding integrand and the value of the improper integral. Enter inf for ol, -inf for -00, and DNE if the limit does not exist. Compare with a dr = By the Integral Test, 7 Inn the infinite series Σ n? -2 A. converges B. diverges Note: You can earn partial credit on this problem. Preview Answers...
Use the integral test to determine whether the series converges. Show all work to justify your answer. vands n=1 Select one: O A. diverges O B. converges