Question

[1.02/7.14 Points] DETAILS PREVIOUS ANSWERS SCALCETS 11.3.512.XP.MI.SA. MY NOT This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Use the Integral Test to determine whether the series convergent or divergent. Step In order to apply the Integral Test for the function f(x) on the interval (a, :), It must be true that (Select all that apply.) must be continuous. f must be differentiable. must be positive must be negative. I must be increasing. Pfmust be decreasing, Step 2 For ne-130, Rx) = xe 13 is continuous, positive, and decreasing on [1,x). We consider the following. Using Integration by parts with u = x and av - e-!ox, we get e-13 dx = lim ]x] Submit Skin (you cannot come back) Need Help? Read it Talk to a Tutor Suur Answer

Answer 1

Stepti f must ། must be continuous. be positive. De decreasing f must Step 2: 13x dr = lim xe-13x de be L lim bo 13 6132 169613x Step 3. lim be -b é 136 13 -6 13 e 136 0-00 dim - -1 136 By l'hospital Rule tsoo 16ge lo can see that, Step TV Now you lim 1700 13 -136 le 136 e et i 13 + e-13) 169 169 * o - Att O + 14 169 >> 14 189813 Series is convergence.