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Question

Evaluate limx1n+e1nn+e2nn+e3nn+...+en1nn.

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Solution

limx1n+e1nn+e2nn+e3nn+...+en1nn

=limx1n[1+e1n+e2n+e3n+...+en1n]

=limx1n+limx[e1n+e2n+e3n+...+en1n]

=0+limx1nnr=1ern by using the definition of integral we have

=10exdx=[ex]10=e1e0=e1

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