# Using Riemann sums, find integral representations of the following:?

##
(1) #lim_(nrarroo)sum_(i=1)^n 2e^sqrt(i/n)1/n #

(2) #lim_(nrarroo)sum_(i=1)^n (i/n)^27 * 1/n#

(1)

(2)

Please see below for (1).

We have

and we get

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Please see below for (2).

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Sure, I'd be happy to help. Could you please provide the function or the expression for which you'd like to find integral representations using Riemann sums?

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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