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Integration and Limits Proof

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If a>0 show that pi
lim ∫sin(nx)/nx dx = 0
a
What happens if a = 0.

The problem in the file submitted is from an undergraduate course in Real Analysis. If you are able to work the problems, please detail any theorems or lemmas used in your solutions. The book we are using is titled "The Elements of Real Analysis" by Robert G. Bartle. We are working on derivatives and integrals, but have not started infinite series.

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An integration and limits proof is provided and discussed. The solution is detailed and well presented.

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