3. (6 marks total; 3 marks each) a) Use the Integral Test to show that the...
6. We want to use the Integral Test to show that the positive series a converges. All of the following need to be done except one. Which is the one we don't need to do? (a) Find a function f(x) defined on [1,00) such that f(x) > 0, f(x) is decreasing, and f(n) = a, for all n. (b) Show that ſ f(z) dr converges. (e) Show that lim Ss6 f(x) dx exists. (d) Show that lim sexists. 7. Suppose...
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...
(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 ----
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....
Page < 2 > of 3 ZOOM 3. Use the Integral Test or a Comparison Test to determine if the series shown below converges or diverges. Be sure to check that the conditions of the Integral Test or Comparison Test are satisfied. 4" (sin 4"(sin(n) + 1) 22-1
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
please show all steps
Use the Integral Test to determine the convergence or divergence of the following series, or state that the test does not apply. 2 Σ k(Ink)? k= 3 Select the correct choice below and, if necessary, fill in the answer box to complete the choice. O A. 2. The series converges. The value of the integralſ dx is x(In x)2 (Type an exact answer.) B. 2 The series diverges. The value of the integralſ -dx is x(...
9.3 Integral Test & Seric Use the Integral Test to determine the convergence or divergence of the series. 2 3n + 6 n = 1 Part 1 of 5 Recall the Integral Test. Iff is positive positive, continuous, and decreasing decreasing for x 2 1 and an = f(n), then an and f(x) dx either both converge or both diverge. n=1 Part 2 of 5 Let f(x) 2 3x + 6 Note that f(x) is positive, continuous, and decreasing for...
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5. Use the integral test and the root test to determine whether the series converges. 1 2 al Ext(n) (+) (b) È C +3)* (14 pts) 6. Determine whether the series is absolutoly conrormont condition 11
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