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# Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined on $[0, 1]$.$\displaystyle \lim_{n \to \infty} \sum_{i = 1}^n \biggl( \frac{i^4}{n^5} + \frac{i}{n^2} \biggr)$

## $$\frac{7}{10}$$

Integrals

Integration

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

okay, We know that Delta acts. In other words, changing axes. One of her on and a zero knew the formula for Delta X's B minus over end. So Bemis here, over, and somebody we know A is zero, which gives us one of her and therefore we know the hostage equivalent to one. Therefore, what we know is that we have the integral from zero 21 of X the fourth plus ax detox integrate increase the exploited by one divide by the new exponents increase to divide by two. Our solution is seven tons.

#### Topics

Integrals

Integration

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp