BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

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

lim n   i = 1 n ( i 4 n 5 + i n 2 )

To determine

To evaluate:

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

Explanation

1) Concept:

i) Riemann sum:

If is f is integrable on [a, b], then

abfxdx=limni=1nfxi x

where,

x= b-an and xi=a+i x

f(x) is called as integrand, n is the number of sub intervals,  a is the lower limit and b is the upper limit.

ii) If f is continuous on [a, b], then

abf(x) dx=Fb-F(a)

where, F is any anti derivative of f,

3) Given:

limni=1ni4n5+in2

4) Calculation:

Factor out 1n  from the given expression

limni=1ni4n4+in·1n

Rewriting,

limni=1n0+i4n4+in·1n

Hence,

a=0,x=1n

x= b-an

1n= b-0n

1= b

Therefore,   b=1

xi=a+i x

xi=0+i1n=in

Let x=in then

i4n4+in=<

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started
Sect-4.1 P-11ESect-4.1 P-12ESect-4.1 P-13ESect-4.1 P-14ESect-4.1 P-15ESect-4.1 P-16ESect-4.1 P-17ESect-4.1 P-18ESect-4.1 P-19ESect-4.1 P-20ESect-4.1 P-21ESect-4.1 P-22ESect-4.1 P-23ESect-4.1 P-24ESect-4.1 P-25ESect-4.1 P-26ESect-4.1 P-27ESect-4.1 P-28ESect-4.1 P-29ESect-4.1 P-30ESect-4.1 P-31ESect-4.1 P-32ESect-4.2 P-1ESect-4.2 P-2ESect-4.2 P-3ESect-4.2 P-4ESect-4.2 P-5ESect-4.2 P-6ESect-4.2 P-7ESect-4.2 P-8ESect-4.2 P-9ESect-4.2 P-10ESect-4.2 P-11ESect-4.2 P-12ESect-4.2 P-13ESect-4.2 P-14ESect-4.2 P-15ESect-4.2 P-16ESect-4.2 P-17ESect-4.2 P-18ESect-4.2 P-19ESect-4.2 P-20ESect-4.2 P-21ESect-4.2 P-22ESect-4.2 P-23ESect-4.2 P-24ESect-4.2 P-25ESect-4.2 P-26ESect-4.2 P-27ESect-4.2 P-28ESect-4.2 P-29ESect-4.2 P-30ESect-4.2 P-31ESect-4.2 P-32ESect-4.2 P-33ESect-4.2 P-34ESect-4.2 P-35ESect-4.2 P-36ESect-4.2 P-37ESect-4.2 P-38ESect-4.2 P-39ESect-4.2 P-40ESect-4.2 P-41ESect-4.2 P-42ESect-4.2 P-43ESect-4.2 P-44ESect-4.2 P-45ESect-4.2 P-46ESect-4.2 P-47ESect-4.2 P-48ESect-4.2 P-49ESect-4.2 P-50ESect-4.2 P-51ESect-4.2 P-52ESect-4.2 P-53ESect-4.2 P-54ESect-4.2 P-55ESect-4.2 P-56ESect-4.2 P-57ESect-4.2 P-58ESect-4.2 P-59ESect-4.2 P-60ESect-4.2 P-61ESect-4.2 P-62ESect-4.2 P-63ESect-4.2 P-64ESect-4.2 P-65ESect-4.2 P-66ESect-4.2 P-67ESect-4.2 P-68ESect-4.2 P-69ESect-4.2 P-70ESect-4.2 P-71ESect-4.2 P-72ESect-4.2 P-73ESect-4.2 P-74ESect-4.2 P-75ESect-4.3 P-1ESect-4.3 P-2ESect-4.3 P-3ESect-4.3 P-4ESect-4.3 P-5ESect-4.3 P-6ESect-4.3 P-7ESect-4.3 P-8ESect-4.3 P-9ESect-4.3 P-10ESect-4.3 P-11ESect-4.3 P-12ESect-4.3 P-13ESect-4.3 P-14ESect-4.3 P-15ESect-4.3 P-16ESect-4.3 P-17ESect-4.3 P-18ESect-4.3 P-19ESect-4.3 P-20ESect-4.3 P-21ESect-4.3 P-22ESect-4.3 P-23ESect-4.3 P-24ESect-4.3 P-25ESect-4.3 P-26ESect-4.3 P-27ESect-4.3 P-28ESect-4.3 P-29ESect-4.3 P-30ESect-4.3 P-31ESect-4.3 P-32ESect-4.3 P-33ESect-4.3 P-34ESect-4.3 P-35ESect-4.3 P-36ESect-4.3 P-37ESect-4.3 P-38ESect-4.3 P-39ESect-4.3 P-40ESect-4.3 P-41ESect-4.3 P-42ESect-4.3 P-43ESect-4.3 P-44ESect-4.3 P-45ESect-4.3 P-46ESect-4.3 P-47ESect-4.3 P-48ESect-4.3 P-49ESect-4.3 P-50ESect-4.3 P-51ESect-4.3 P-52ESect-4.3 P-53ESect-4.3 P-54ESect-4.3 P-55ESect-4.3 P-56ESect-4.3 P-57ESect-4.3 P-58ESect-4.3 P-59ESect-4.3 P-60ESect-4.3 P-61ESect-4.3 P-62ESect-4.3 P-63ESect-4.3 P-64ESect-4.3 P-65ESect-4.3 P-66ESect-4.3 P-67ESect-4.3 P-68ESect-4.3 P-69ESect-4.3 P-70ESect-4.3 P-71ESect-4.3 P-72ESect-4.3 P-73ESect-4.3 P-74ESect-4.3 P-75ESect-4.3 P-76ESect-4.3 P-77ESect-4.3 P-78ESect-4.3 P-79ESect-4.3 P-80ESect-4.3 P-81ESect-4.3 P-82ESect-4.3 P-83ESect-4.3 P-84ESect-4.4 P-1ESect-4.4 P-2ESect-4.4 P-3ESect-4.4 P-4ESect-4.4 P-5ESect-4.4 P-6ESect-4.4 P-7ESect-4.4 P-8ESect-4.4 P-9ESect-4.4 P-10ESect-4.4 P-11ESect-4.4 P-12ESect-4.4 P-13ESect-4.4 P-14ESect-4.4 P-15ESect-4.4 P-16ESect-4.4 P-17ESect-4.4 P-18ESect-4.4 P-19ESect-4.4 P-20ESect-4.4 P-21ESect-4.4 P-22ESect-4.4 P-23ESect-4.4 P-24ESect-4.4 P-25ESect-4.4 P-26ESect-4.4 P-27ESect-4.4 P-28ESect-4.4 P-29ESect-4.4 P-30ESect-4.4 P-31ESect-4.4 P-32ESect-4.4 P-33ESect-4.4 P-34ESect-4.4 P-35ESect-4.4 P-36ESect-4.4 P-37ESect-4.4 P-38ESect-4.4 P-39ESect-4.4 P-40ESect-4.4 P-41ESect-4.4 P-42ESect-4.4 P-43ESect-4.4 P-44ESect-4.4 P-45ESect-4.4 P-46ESect-4.4 P-47ESect-4.4 P-48ESect-4.4 P-49ESect-4.4 P-50ESect-4.4 P-51ESect-4.4 P-52ESect-4.4 P-53ESect-4.4 P-54ESect-4.4 P-55ESect-4.4 P-56ESect-4.4 P-57ESect-4.4 P-58ESect-4.4 P-59ESect-4.4 P-60ESect-4.4 P-61ESect-4.4 P-62ESect-4.4 P-63ESect-4.4 P-64ESect-4.4 P-65ESect-4.4 P-66ESect-4.4 P-67ESect-4.4 P-68ESect-4.4 P-69ESect-4.4 P-70ESect-4.4 P-71ESect-4.4 P-72ESect-4.4 P-73ESect-4.4 P-74ESect-4.5 P-1ESect-4.5 P-2ESect-4.5 P-3ESect-4.5 P-4ESect-4.5 P-5ESect-4.5 P-6ESect-4.5 P-7ESect-4.5 P-8ESect-4.5 P-9ESect-4.5 P-10ESect-4.5 P-11ESect-4.5 P-12ESect-4.5 P-13ESect-4.5 P-14ESect-4.5 P-15ESect-4.5 P-16ESect-4.5 P-17ESect-4.5 P-18ESect-4.5 P-19ESect-4.5 P-20ESect-4.5 P-21ESect-4.5 P-22ESect-4.5 P-23ESect-4.5 P-24ESect-4.5 P-25ESect-4.5 P-26ESect-4.5 P-27ESect-4.5 P-28ESect-4.5 P-29ESect-4.5 P-30ESect-4.5 P-31ESect-4.5 P-32ESect-4.5 P-33ESect-4.5 P-34ESect-4.5 P-35ESect-4.5 P-36ESect-4.5 P-37ESect-4.5 P-38ESect-4.5 P-39ESect-4.5 P-40ESect-4.5 P-41ESect-4.5 P-42ESect-4.5 P-43ESect-4.5 P-44ESect-4.5 P-45ESect-4.5 P-46ESect-4.5 P-47ESect-4.5 P-48ESect-4.5 P-49ESect-4.5 P-50ESect-4.5 P-51ESect-4.5 P-52ESect-4.5 P-53ESect-4.5 P-54ESect-4.5 P-55ESect-4.5 P-56ESect-4.5 P-57ESect-4.5 P-58ESect-4.5 P-59ESect-4.5 P-60ESect-4.5 P-61ESect-4.5 P-62ESect-4.5 P-63ESect-4.5 P-64ESect-4.5 P-65ESect-4.5 P-66ESect-4.5 P-67ESect-4.5 P-68ESect-4.5 P-69ESect-4.5 P-70ESect-4.5 P-71ESect-4.5 P-72ESect-4.5 P-73ESect-4.5 P-74ESect-4.5 P-75ESect-4.5 P-76ESect-4.5 P-77ESect-4.5 P-78ESect-4.5 P-79ESect-4.5 P-80ESect-4.5 P-81ESect-4.5 P-82ESect-4.5 P-83ESect-4.5 P-84ESect-4.5 P-85ESect-4.R P-1CCSect-4.R P-2CCSect-4.R P-3CCSect-4.R P-4CCSect-4.R P-5CCSect-4.R P-6CCSect-4.R P-7CCSect-4.R P-8CCSect-4.R P-9CCSect-4.R P-1TFQSect-4.R P-2TFQSect-4.R P-3TFQSect-4.R P-4TFQSect-4.R P-5TFQSect-4.R P-6TFQSect-4.R P-7TFQSect-4.R P-8TFQSect-4.R P-9TFQSect-4.R P-10TFQSect-4.R P-11TFQSect-4.R P-12TFQSect-4.R P-13TFQSect-4.R P-14TFQSect-4.R P-15TFQSect-4.R P-16TFQSect-4.R P-17TFQSect-4.R P-18TFQSect-4.R P-1ESect-4.R P-2ESect-4.R P-3ESect-4.R P-4ESect-4.R P-5ESect-4.R P-6ESect-4.R P-7ESect-4.R P-8ESect-4.R P-9ESect-4.R P-10ESect-4.R P-11ESect-4.R P-12ESect-4.R P-13ESect-4.R P-14ESect-4.R P-15ESect-4.R P-16ESect-4.R P-17ESect-4.R P-18ESect-4.R P-19ESect-4.R P-20ESect-4.R P-21ESect-4.R P-22ESect-4.R P-23ESect-4.R P-24ESect-4.R P-25ESect-4.R P-26ESect-4.R P-27ESect-4.R P-28ESect-4.R P-29ESect-4.R P-30ESect-4.R P-31ESect-4.R P-32ESect-4.R P-33ESect-4.R P-34ESect-4.R P-35ESect-4.R P-36ESect-4.R P-37ESect-4.R P-38ESect-4.R P-39ESect-4.R P-40ESect-4.R P-41ESect-4.R P-42ESect-4.R P-43ESect-4.R P-44ESect-4.R P-45ESect-4.R P-46ESect-4.R P-47ESect-4.R P-48ESect-4.R P-49ESect-4.R P-50ESect-4.R P-51ESect-4.R P-52ESect-4.R P-53ESect-4.R P-54ESect-4.R P-55ESect-4.R P-56ESect-4.R P-57ESect-4.R P-58ESect-4.P P-1PSect-4.P P-2PSect-4.P P-3PSect-4.P P-4PSect-4.P P-5PSect-4.P P-6PSect-4.P P-7PSect-4.P P-8PSect-4.P P-9PSect-4.P P-10PSect-4.P P-11PSect-4.P P-12PSect-4.P P-13PSect-4.P P-14PSect-4.P P-15PSect-4.P P-16PSect-4.P P-17PSect-4.P P-18P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

In Exercises 1316, find the distance between the given pairs of points. (1,1)and(2,2)

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 39-50, sketch the graph of the function with the given rule. Find the domain and range of the func...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Find the interval of convergence of n=1n3xn and find its sum.

Single Variable Calculus: Early Transcendentals

In Exercises 1-22, evaluate the given expression. P(7,7)

Finite Mathematics for the Managerial, Life, and Social Sciences

The best approximation of y using differentials for y = x2 4x at x = 6 when x = dx = 0.03 is: a) 0.36 b) 0.24 ...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Define the reliability of measurement and explain why and how it is measured.

Research Methods for the Behavioral Sciences (MindTap Course List)