Science:Math Exam Resources/Courses/MATH103/April 2017/Question 01 (c)/Solution 1

From UBC Wiki

(i) Since the integrand has an infinite discontinuity at , the integral is defined using a one-sided limit, which can be evaluated as follows.

Therefore, the integral diverges.

(ii) For all positive , we have . Hence the integral converges by comparison to the integral .

(iii) For all , we have , which implies that . Therefore , so the integral converges by comparison to the integral .

(iv) Since , the integral diverges by comparison to the integral .


The complete table is as follows.

converging diverging
(i) no yes
(ii) yes no
(iii) yes no
(iv) no yes