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MATH 1310.03F A Quiz 6 Thursday, November 2, 2000

NAME:

Student Number:tex2html_wrap_inline119 No.tex2html_wrap_inline121Marks tex2html_wrap_inline123


(25 Marks) Discuss the convergence of the following improper integral.
displaymath125

Solution.

1. When q=1, tex2html_wrap_inline131. Hence, we have
displaymath133

and tex2html_wrap_inline135. This implies tex2html_wrap_inline137 and tex2html_wrap_inline139 diverges.

2. When q>1, we have tex2html_wrap_inline145 Let tex2html_wrap_inline147. Then
displaymath149

So, we have
displaymath151

Hence, tex2html_wrap_inline153. The integral tex2html_wrap_inline155 converges.




Kunquan Lan
Thu Nov 2 13:07:16 EST 2000