Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Justify (3) for the case $ h < 0 $.

01:02

Question

Answered step-by-step

Problem 76 Hard Difficulty

Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined on $ [0, 1] $.

$ \displaystyle \lim_{n \to \infty} \frac{1}{n} \biggl( \sqrt{\frac{1}{n}} + \sqrt{\frac{2}{n}} + \sqrt{\frac{3}{n}} + \cdots + \sqrt{\frac{n}{n}} \biggr) $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Bobby Barnes
University of North Texas

Like

Report

Textbook Answer

Official textbook answer

Video by Bobby Barnes

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

01:07

Frank Lin

00:49

Amrita Bhasin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Related Topics

Integrals

Integration

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Grace He
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

05:53

Integrals - Intro

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.

Video Thumbnail

40:35

Area Under Curves - Overview

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.

Join Course
Recommended Videos

00:37

Evaluate the limit by firs…

00:43

Evaluate the limit by firs…

01:26

Express the given limit of…

00:52

Evaluate the limit by firs…

01:02

Evaluate the limit by firs…

01:07

Express the given limit of…

01:51

Calculate
$$\lim _{n \r…

Watch More Solved Questions in Chapter 5

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86

Video Transcript

So they first want us to rewrite this as a Remond some s. So let's go ahead and do that. So this would be the limit as it approaches infinity of one of her. And now that was the thing that's changing is the power in the art of the numerator here. So it's like 123 and just kind of keeps increasing world. The denominator always stays in. So this is gonna be the sum from I is equal to one. Or actually, I guess we would start from zero. Um because I would be the same thing to in of the square root of I over in. And now this. If we were to go ahead and pull this one of her in inside so little limit as an approach to the affinity of the some from I 020 to in off one over in hi over in notice that this is now in the form of If so, if we're on 01 this is like B minus a over in where B is one a zero. So this is Delta X eso There's just one my zero over in which is one or in. So that's our Delta X Here, This is Delta X, and then this function is going to be like X I because it's just going to be our Delta X plus R a Oh, Delta x times I like that. Um, yeah, so you could see how. Okay, well, we have one over in times I and then plus zero so that there is Route X, I and so. But this is really going to say is that this is equal to the integral from zero to one of the square root of X dx. And now we can go ahead and evaluate this using power rule truck, my pin. So remember, we can rewrite this as a one half power. So powerful says, add one to the power, so it's gonna be x 23 house, and then we divide by the new power relapse. Then we evaluate this from 0 to 1. Um, so that would just be two thirds next to the three half evaluated from 01 So we plug in one, so be two thirds times one minus two thirds times zero. So that's just zero. So we end up where that infinite limit ends up being equal to two thirds

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
67
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
43
Hosted by: Alonso M
See More

Related Topics

Integrals

Integration

Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

05:53

Integrals - Intro

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.

Video Thumbnail

40:35

Area Under Curves - Overview

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.

Join Course
Recommended Videos

00:37

Evaluate the limit by first recognizing the sum as a Riemann sum for a function…

00:43

Evaluate the limit by first recognizing the sum as a Riemann sum for a function…

01:26

Express the given limit of a Riemann sum as a definite integral and then evalua…

00:52

Evaluate the limit by first recognizing the sum as a Riemann sum for a function…

01:02

Evaluate the limit by first recognizing the sum as a Riemann sum for a function…

01:07

Express the given limit of a Riemann sum as a definite integral and then evalua…

01:51

Calculate $$\lim _{n \rightarrow \infty}\left[\frac{1}{n+1}+\frac{1}{n+2}+\cdot…
Additional Mathematics Questions

02:15

Consider the numbers{11, 9, 5, 6, 13, 12, 17}.In how many ways can I order t…

01:37

Consider the following statement: "As the economy improved in our state…

02:28

The probability that Ama wakes up before her alarm rings is 0.4. a. Find the…

03:03

Statistics QuestionsWhen a researcher uses a random sample of 400 to make co…

01:47

Using everyday knowledge, which of the following statements is an if-then…

02:14

Task 1Overview:Dear writer, you are to provide solutions for the following p…

04:37

The Metropolitan Bus Company claims that the mean waiting time for a bus dur…

03:45

The time a patient has to wait to see a doctor in the emergency room is ass…

03:00

Consider all six-digit numbers that can be created from the digits 0-9 where…

01:56

1. A golfer drops a ball to replace one lost in a water hazard. With upw…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started