- #1
BobSun
- 4
- 0
Limit of an integral
1. Homework Statement
Evaluate:
the limit as n goes to [tex]\infty[/tex] of
[tex]\int^{1}_{0} (n^{3/2}x^{5/4})/(1+n^{2}x^{2})dx[/tex]
dx is the lebesgue measure
2. Homework Equations
I thought I could use the monotone convergence theorem or the dominated convergence theorem neither work.
3. The Attempt at a Solution
the intregrand is dominated by [tex]1/\sqrt{x}[/tex] but [tex]1/\sqrt{x}[/tex] isn't lebesgue integrable.
1. Homework Statement
Evaluate:
the limit as n goes to [tex]\infty[/tex] of
[tex]\int^{1}_{0} (n^{3/2}x^{5/4})/(1+n^{2}x^{2})dx[/tex]
dx is the lebesgue measure
2. Homework Equations
I thought I could use the monotone convergence theorem or the dominated convergence theorem neither work.
3. The Attempt at a Solution
the intregrand is dominated by [tex]1/\sqrt{x}[/tex] but [tex]1/\sqrt{x}[/tex] isn't lebesgue integrable.