The following function is defined for all , and is a positive integer. Prove or provide a counterexample to the following statement.

Assume

Then

**Incomplete.**

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Stumbling Robot

A Fraction of a Dot
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Prove or disprove: If *lim f(x) = 0* and *lim I*_{n} = A then *∫ f(x)* converges to *A*

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### Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):

The following function is defined for all , and is a positive integer. Prove or provide a counterexample to the following statement.

Assume

Then

**Incomplete.**

Proof. For some positive real such that , we have

where . But as and hence , , and thus . But we know , which implies . Thus, we have shown that

This completes the proof.

Sorry guys, I forgot to change letters for the dummy variables as x goes to infinity.