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Compute the given limit.$$\lim _{n \rightarrow \infty} \frac{2}{n} \sum_{i=1}^{n}\left(3+\left(\frac{i}{n}\right)^{2}\right)$$

$$20 / 3$$

00:42

Christopher S.

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 5

Sigma Notation and Areas

Integrals

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

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Find limit

Hello, here we have the limit as N tends to infinity of one plus three over and always to the to end. So we know that E is equal to the limit as let's say, T tends to infinity of one plus one over T to the T. So um here we're going to get to the limit um is going to be equal to, well we can write this as the limit as N tends to infinity of one plus three over N to the end, which is equal to E cubed times E cubed. So therefore our limit is going to be equal to E to the sixth power.

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