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

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(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)

##### 2 Answers

#### Answer

#### Answer:

#### Explanation

#### Explanation:

#### Answer:

Please see below for (2).

#### Explanation:

Using

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

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

#### Answer

#### Answer:

#### Explanation

#### Explanation:

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#### Answer:

Please see below for (1).

#### Explanation:

Using

So

has

So

Observe that when

In this case we get

We have

# lim_(nrarroo)sum_(i=1)^n 2e^sqrt(0+i/n) 1/n#

So

and we get

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