Practice Theory Question

1. Test for convergence the improper integral

2.     Show that the integral

3.     Test for convergence the improper integral

4.     Test for convergence the improper integral

5.     Show the convergence using Abel’s test

6.     Prove  that =

7.     Prove that 

8.     Compute  the  value ?

9.     Express in terms of gamma function

10. Compute ?

11. Prove that  

12. Prove that .

13. Prove that