BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

Solutions

Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

(a) Evaluate lim x x sin 1 x .

(b) Evaluate lim x 0 x sin 1 x .

(c) Illustrate parts (a) and (b) by graphing y = xsin( 1/x).

(a)

To determine

To evaluate: The value of limxxsin1x.

Explanation

Result used:

The limit of limx0sinxx=1

Calculation:

Compute limxxsin1x.

limxxsin1x=limx sin1x  1x

Substitute 1x for θ, then θ will approach to 0 as x approaches

(b)

To determine

To evaluate: The value of limx0xsin1x.

(c)

To determine

To sketch: The graph of the function y=xsin(1x).

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-3.1 P-11ESect-3.1 P-12ESect-3.1 P-13ESect-3.1 P-14ESect-3.1 P-15ESect-3.1 P-16ESect-3.1 P-17ESect-3.1 P-18ESect-3.1 P-19ESect-3.1 P-20ESect-3.1 P-21ESect-3.1 P-22ESect-3.1 P-23ESect-3.1 P-24ESect-3.1 P-25ESect-3.1 P-26ESect-3.1 P-27ESect-3.1 P-28ESect-3.1 P-29ESect-3.1 P-30ESect-3.1 P-31ESect-3.1 P-32ESect-3.1 P-33ESect-3.1 P-34ESect-3.1 P-35ESect-3.1 P-36ESect-3.1 P-37ESect-3.1 P-38ESect-3.1 P-39ESect-3.1 P-40ESect-3.1 P-41ESect-3.1 P-42ESect-3.1 P-43ESect-3.1 P-44ESect-3.1 P-45ESect-3.1 P-46ESect-3.1 P-47ESect-3.1 P-48ESect-3.1 P-49ESect-3.1 P-50ESect-3.1 P-51ESect-3.1 P-52ESect-3.1 P-53ESect-3.1 P-55ESect-3.1 P-56ESect-3.1 P-57ESect-3.1 P-58ESect-3.1 P-59ESect-3.1 P-60ESect-3.1 P-61ESect-3.1 P-62ESect-3.1 P-63ESect-3.1 P-64ESect-3.1 P-65ESect-3.1 P-66ESect-3.1 P-67ESect-3.1 P-68ESect-3.1 P-69ESect-3.1 P-70ESect-3.1 P-71ESect-3.1 P-72ESect-3.1 P-73ESect-3.1 P-74ESect-3.1 P-75ESect-3.1 P-76ESect-3.1 P-77ESect-3.1 P-78ESect-3.1 P-79ESect-3.1 P-80ESect-3.1 P-81ESect-3.1 P-82ESect-3.1 P-83ESect-3.1 P-84ESect-3.1 P-85ESect-3.1 P-86ESect-3.2 P-1ESect-3.2 P-2ESect-3.2 P-3ESect-3.2 P-4ESect-3.2 P-5ESect-3.2 P-6ESect-3.2 P-7ESect-3.2 P-8ESect-3.2 P-9ESect-3.2 P-10ESect-3.2 P-11ESect-3.2 P-12ESect-3.2 P-13ESect-3.2 P-14ESect-3.2 P-15ESect-3.2 P-16ESect-3.2 P-17ESect-3.2 P-18ESect-3.2 P-19ESect-3.2 P-20ESect-3.2 P-21ESect-3.2 P-22ESect-3.2 P-23ESect-3.2 P-24ESect-3.2 P-25ESect-3.2 P-26ESect-3.2 P-27ESect-3.2 P-28ESect-3.2 P-29ESect-3.2 P-30ESect-3.2 P-31ESect-3.2 P-32ESect-3.2 P-33ESect-3.2 P-34ESect-3.2 P-35ESect-3.2 P-36ESect-3.2 P-37ESect-3.2 P-38ESect-3.2 P-39ESect-3.2 P-40ESect-3.2 P-41ESect-3.2 P-42ESect-3.2 P-43ESect-3.2 P-44ESect-3.2 P-45ESect-3.2 P-46ESect-3.2 P-47ESect-3.2 P-48ESect-3.2 P-49ESect-3.2 P-50ESect-3.2 P-51ESect-3.2 P-52ESect-3.2 P-53ESect-3.2 P-54ESect-3.2 P-55ESect-3.2 P-56ESect-3.2 P-57ESect-3.2 P-58ESect-3.2 P-59ESect-3.2 P-60ESect-3.2 P-61ESect-3.2 P-62ESect-3.2 P-63ESect-3.2 P-64ESect-3.3 P-1ESect-3.3 P-2ESect-3.3 P-3ESect-3.3 P-4ESect-3.3 P-5ESect-3.3 P-6ESect-3.3 P-7ESect-3.3 P-8ESect-3.3 P-9ESect-3.3 P-10ESect-3.3 P-11ESect-3.3 P-12ESect-3.3 P-13ESect-3.3 P-14ESect-3.3 P-15ESect-3.3 P-16ESect-3.3 P-17ESect-3.3 P-18ESect-3.3 P-19ESect-3.3 P-20ESect-3.3 P-21ESect-3.3 P-22ESect-3.3 P-23ESect-3.3 P-24ESect-3.3 P-25ESect-3.3 P-26ESect-3.3 P-27ESect-3.3 P-28ESect-3.3 P-29ESect-3.3 P-30ESect-3.3 P-31ESect-3.3 P-32ESect-3.3 P-33ESect-3.3 P-34ESect-3.3 P-35ESect-3.3 P-36ESect-3.3 P-37ESect-3.3 P-38ESect-3.3 P-39ESect-3.3 P-40ESect-3.3 P-41ESect-3.3 P-42ESect-3.3 P-43ESect-3.3 P-44ESect-3.3 P-45ESect-3.3 P-46ESect-3.3 P-47ESect-3.3 P-48ESect-3.3 P-49ESect-3.3 P-50ESect-3.3 P-51ESect-3.3 P-52ESect-3.3 P-53ESect-3.3 P-54ESect-3.3 P-55ESect-3.3 P-56ESect-3.3 P-57ESect-3.3 P-58ESect-3.4 P-1ESect-3.4 P-2ESect-3.4 P-3ESect-3.4 P-4ESect-3.4 P-5ESect-3.4 P-6ESect-3.4 P-7ESect-3.4 P-8ESect-3.4 P-9ESect-3.4 P-10ESect-3.4 P-11ESect-3.4 P-12ESect-3.4 P-13ESect-3.4 P-14ESect-3.4 P-15ESect-3.4 P-16ESect-3.4 P-17ESect-3.4 P-18ESect-3.4 P-19ESect-3.4 P-20ESect-3.4 P-21ESect-3.4 P-22ESect-3.4 P-23ESect-3.4 P-24ESect-3.4 P-25ESect-3.4 P-26ESect-3.4 P-27ESect-3.4 P-28ESect-3.4 P-29ESect-3.4 P-30ESect-3.4 P-31ESect-3.4 P-32ESect-3.4 P-33ESect-3.4 P-34ESect-3.4 P-35ESect-3.4 P-36ESect-3.4 P-37ESect-3.4 P-38ESect-3.4 P-39ESect-3.4 P-40ESect-3.4 P-41ESect-3.4 P-42ESect-3.4 P-43ESect-3.4 P-44ESect-3.4 P-45ESect-3.4 P-46ESect-3.4 P-47ESect-3.4 P-48ESect-3.4 P-49ESect-3.4 P-50ESect-3.4 P-51ESect-3.4 P-52ESect-3.4 P-53ESect-3.4 P-54ESect-3.4 P-55ESect-3.4 P-56ESect-3.4 P-57ESect-3.4 P-58ESect-3.4 P-59ESect-3.4 P-60ESect-3.4 P-61ESect-3.4 P-62ESect-3.4 P-63ESect-3.4 P-64ESect-3.4 P-65ESect-3.4 P-66ESect-3.4 P-67ESect-3.4 P-68ESect-3.4 P-69ESect-3.4 P-70ESect-3.4 P-71ESect-3.4 P-72ESect-3.4 P-73ESect-3.4 P-74ESect-3.4 P-75ESect-3.4 P-76ESect-3.4 P-77ESect-3.4 P-78ESect-3.4 P-79ESect-3.4 P-80ESect-3.4 P-81ESect-3.4 P-82ESect-3.4 P-83ESect-3.4 P-84ESect-3.4 P-85ESect-3.4 P-86ESect-3.4 P-87ESect-3.4 P-88ESect-3.4 P-89ESect-3.4 P-90ESect-3.4 P-93ESect-3.4 P-94ESect-3.4 P-95ESect-3.4 P-96ESect-3.4 P-97ESect-3.4 P-98ESect-3.4 P-99ESect-3.4 P-100ESect-3.5 P-1ESect-3.5 P-2ESect-3.5 P-3ESect-3.5 P-4ESect-3.5 P-5ESect-3.5 P-6ESect-3.5 P-7ESect-3.5 P-8ESect-3.5 P-9ESect-3.5 P-10ESect-3.5 P-11ESect-3.5 P-12ESect-3.5 P-13ESect-3.5 P-14ESect-3.5 P-15ESect-3.5 P-16ESect-3.5 P-17ESect-3.5 P-18ESect-3.5 P-19ESect-3.5 P-20ESect-3.5 P-21ESect-3.5 P-22ESect-3.5 P-23ESect-3.5 P-24ESect-3.5 P-25ESect-3.5 P-26ESect-3.5 P-27ESect-3.5 P-28ESect-3.5 P-29ESect-3.5 P-30ESect-3.5 P-31ESect-3.5 P-32ESect-3.5 P-33ESect-3.5 P-34ESect-3.5 P-35ESect-3.5 P-36ESect-3.5 P-37ESect-3.5 P-38ESect-3.5 P-39ESect-3.5 P-40ESect-3.5 P-43ESect-3.5 P-44ESect-3.5 P-45ESect-3.5 P-46ESect-3.5 P-47ESect-3.5 P-48ESect-3.5 P-49ESect-3.5 P-50ESect-3.5 P-51ESect-3.5 P-52ESect-3.5 P-53ESect-3.5 P-54ESect-3.5 P-55ESect-3.5 P-56ESect-3.5 P-57ESect-3.5 P-58ESect-3.5 P-59ESect-3.5 P-60ESect-3.5 P-61ESect-3.5 P-62ESect-3.5 P-63ESect-3.5 P-64ESect-3.5 P-65ESect-3.5 P-66ESect-3.5 P-67ESect-3.5 P-68ESect-3.5 P-69ESect-3.5 P-70ESect-3.5 P-71ESect-3.5 P-73ESect-3.5 P-74ESect-3.5 P-75ESect-3.5 P-76ESect-3.5 P-77ESect-3.5 P-78ESect-3.5 P-79ESect-3.5 P-80ESect-3.6 P-1ESect-3.6 P-2ESect-3.6 P-3ESect-3.6 P-4ESect-3.6 P-5ESect-3.6 P-6ESect-3.6 P-7ESect-3.6 P-8ESect-3.6 P-9ESect-3.6 P-10ESect-3.6 P-11ESect-3.6 P-12ESect-3.6 P-13ESect-3.6 P-14ESect-3.6 P-15ESect-3.6 P-16ESect-3.6 P-17ESect-3.6 P-18ESect-3.6 P-19ESect-3.6 P-20ESect-3.6 P-21ESect-3.6 P-22ESect-3.6 P-23ESect-3.6 P-24ESect-3.6 P-25ESect-3.6 P-26ESect-3.6 P-27ESect-3.6 P-28ESect-3.6 P-29ESect-3.6 P-30ESect-3.6 P-31ESect-3.6 P-32ESect-3.6 P-33ESect-3.6 P-34ESect-3.6 P-35ESect-3.6 P-36ESect-3.6 P-37ESect-3.6 P-38ESect-3.6 P-39ESect-3.6 P-40ESect-3.6 P-41ESect-3.6 P-42ESect-3.6 P-43ESect-3.6 P-44ESect-3.6 P-45ESect-3.6 P-46ESect-3.6 P-47ESect-3.6 P-48ESect-3.6 P-49ESect-3.6 P-50ESect-3.6 P-51ESect-3.6 P-52ESect-3.6 P-53ESect-3.6 P-54ESect-3.6 P-55ESect-3.6 P-56ESect-3.7 P-1ESect-3.7 P-2ESect-3.7 P-3ESect-3.7 P-4ESect-3.7 P-5ESect-3.7 P-6ESect-3.7 P-7ESect-3.7 P-8ESect-3.7 P-9ESect-3.7 P-10ESect-3.7 P-11ESect-3.7 P-12ESect-3.7 P-13ESect-3.7 P-14ESect-3.7 P-15ESect-3.7 P-16ESect-3.7 P-17ESect-3.7 P-18ESect-3.7 P-19ESect-3.7 P-20ESect-3.7 P-21ESect-3.7 P-22ESect-3.7 P-23ESect-3.7 P-24ESect-3.7 P-25ESect-3.7 P-26ESect-3.7 P-28ESect-3.7 P-29ESect-3.7 P-30ESect-3.7 P-31ESect-3.7 P-32ESect-3.7 P-33ESect-3.7 P-34ESect-3.7 P-35ESect-3.7 P-36ESect-3.7 P-37ESect-3.7 P-38ESect-3.7 P-39ESect-3.8 P-1ESect-3.8 P-2ESect-3.8 P-3ESect-3.8 P-4ESect-3.8 P-5ESect-3.8 P-6ESect-3.8 P-7ESect-3.8 P-8ESect-3.8 P-9ESect-3.8 P-10ESect-3.8 P-11ESect-3.8 P-12ESect-3.8 P-13ESect-3.8 P-14ESect-3.8 P-15ESect-3.8 P-16ESect-3.8 P-17ESect-3.8 P-18ESect-3.8 P-19ESect-3.8 P-20ESect-3.8 P-21ESect-3.8 P-22ESect-3.9 P-1ESect-3.9 P-2ESect-3.9 P-3ESect-3.9 P-4ESect-3.9 P-5ESect-3.9 P-6ESect-3.9 P-7ESect-3.9 P-8ESect-3.9 P-9ESect-3.9 P-10ESect-3.9 P-11ESect-3.9 P-12ESect-3.9 P-13ESect-3.9 P-14ESect-3.9 P-15ESect-3.9 P-16ESect-3.9 P-17ESect-3.9 P-18ESect-3.9 P-19ESect-3.9 P-20ESect-3.9 P-21ESect-3.9 P-22ESect-3.9 P-23ESect-3.9 P-24ESect-3.9 P-25ESect-3.9 P-26ESect-3.9 P-27ESect-3.9 P-28ESect-3.9 P-29ESect-3.9 P-30ESect-3.9 P-31ESect-3.9 P-32ESect-3.9 P-33ESect-3.9 P-34ESect-3.9 P-35ESect-3.9 P-36ESect-3.9 P-37ESect-3.9 P-38ESect-3.9 P-39ESect-3.9 P-40ESect-3.9 P-41ESect-3.9 P-42ESect-3.9 P-43ESect-3.9 P-44ESect-3.9 P-45ESect-3.9 P-46ESect-3.9 P-47ESect-3.9 P-48ESect-3.9 P-49ESect-3.9 P-50ESect-3.10 P-1ESect-3.10 P-2ESect-3.10 P-3ESect-3.10 P-4ESect-3.10 P-5ESect-3.10 P-6ESect-3.10 P-7ESect-3.10 P-8ESect-3.10 P-9ESect-3.10 P-10ESect-3.10 P-11ESect-3.10 P-12ESect-3.10 P-13ESect-3.10 P-14ESect-3.10 P-15ESect-3.10 P-16ESect-3.10 P-17ESect-3.10 P-18ESect-3.10 P-19ESect-3.10 P-20ESect-3.10 P-21ESect-3.10 P-22ESect-3.10 P-23ESect-3.10 P-24ESect-3.10 P-25ESect-3.10 P-26ESect-3.10 P-27ESect-3.10 P-28ESect-3.10 P-29ESect-3.10 P-30ESect-3.10 P-31ESect-3.10 P-32ESect-3.10 P-33ESect-3.10 P-34ESect-3.10 P-35ESect-3.10 P-36ESect-3.10 P-37ESect-3.10 P-38ESect-3.10 P-39ESect-3.10 P-40ESect-3.10 P-41ESect-3.10 P-42ESect-3.10 P-43ESect-3.10 P-44ESect-3.11 P-1ESect-3.11 P-2ESect-3.11 P-3ESect-3.11 P-4ESect-3.11 P-5ESect-3.11 P-6ESect-3.11 P-7ESect-3.11 P-8ESect-3.11 P-9ESect-3.11 P-10ESect-3.11 P-11ESect-3.11 P-12ESect-3.11 P-13ESect-3.11 P-14ESect-3.11 P-15ESect-3.11 P-16ESect-3.11 P-17ESect-3.11 P-18ESect-3.11 P-19ESect-3.11 P-20ESect-3.11 P-21ESect-3.11 P-22ESect-3.11 P-23ESect-3.11 P-24ESect-3.11 P-25ESect-3.11 P-26ESect-3.11 P-27ESect-3.11 P-28ESect-3.11 P-29ESect-3.11 P-30ESect-3.11 P-31ESect-3.11 P-32ESect-3.11 P-33ESect-3.11 P-34ESect-3.11 P-35ESect-3.11 P-36ESect-3.11 P-37ESect-3.11 P-38ESect-3.11 P-39ESect-3.11 P-40ESect-3.11 P-41ESect-3.11 P-42ESect-3.11 P-43ESect-3.11 P-44ESect-3.11 P-45ESect-3.11 P-46ESect-3.11 P-47ESect-3.11 P-48ESect-3.11 P-49ESect-3.11 P-50ESect-3.11 P-51ESect-3.11 P-52ESect-3.11 P-53ESect-3.11 P-54ESect-3.11 P-55ESect-3.11 P-56ESect-3.11 P-57ESect-3.11 P-58ECh-3 P-1RCCCh-3 P-2RCCCh-3 P-3RCCCh-3 P-4RCCCh-3 P-5RCCCh-3 P-6RCCCh-3 P-7RCCCh-3 P-1RQCh-3 P-2RQCh-3 P-3RQCh-3 P-4RQCh-3 P-5RQCh-3 P-6RQCh-3 P-7RQCh-3 P-8RQCh-3 P-9RQCh-3 P-10RQCh-3 P-11RQCh-3 P-12RQCh-3 P-13RQCh-3 P-14RQCh-3 P-15RQCh-3 P-1RECh-3 P-2RECh-3 P-3RECh-3 P-4RECh-3 P-5RECh-3 P-6RECh-3 P-7RECh-3 P-8RECh-3 P-9RECh-3 P-10RECh-3 P-11RECh-3 P-12RECh-3 P-13RECh-3 P-14RECh-3 P-15RECh-3 P-16RECh-3 P-17RECh-3 P-18RECh-3 P-19RECh-3 P-20RECh-3 P-21RECh-3 P-22RECh-3 P-23RECh-3 P-24RECh-3 P-25RECh-3 P-26RECh-3 P-27RECh-3 P-28RECh-3 P-29RECh-3 P-30RECh-3 P-31RECh-3 P-32RECh-3 P-33RECh-3 P-34RECh-3 P-35RECh-3 P-36RECh-3 P-37RECh-3 P-38RECh-3 P-39RECh-3 P-40RECh-3 P-41RECh-3 P-42RECh-3 P-43RECh-3 P-44RECh-3 P-45RECh-3 P-46RECh-3 P-47RECh-3 P-48RECh-3 P-49RECh-3 P-50RECh-3 P-51RECh-3 P-52RECh-3 P-53RECh-3 P-54RECh-3 P-55RECh-3 P-56RECh-3 P-57RECh-3 P-58RECh-3 P-59RECh-3 P-60RECh-3 P-61RECh-3 P-62RECh-3 P-63RECh-3 P-64RECh-3 P-65RECh-3 P-66RECh-3 P-67RECh-3 P-68RECh-3 P-69RECh-3 P-70RECh-3 P-71RECh-3 P-72RECh-3 P-73RECh-3 P-74RECh-3 P-75RECh-3 P-76RECh-3 P-77RECh-3 P-78RECh-3 P-79RECh-3 P-80RECh-3 P-81RECh-3 P-82RECh-3 P-83RECh-3 P-84RECh-3 P-85RECh-3 P-86RECh-3 P-87RECh-3 P-88RECh-3 P-89RECh-3 P-90RECh-3 P-91RECh-3 P-92RECh-3 P-93RECh-3 P-94RECh-3 P-95RECh-3 P-96RECh-3 P-97RECh-3 P-98RECh-3 P-99RECh-3 P-100RECh-3 P-101RECh-3 P-102RECh-3 P-103RECh-3 P-104RECh-3 P-105RECh-3 P-106RECh-3 P-107RECh-3 P-108RECh-3 P-109RECh-3 P-110RECh-3 P-111RECh-3 P-112RECh-3 P-1PCh-3 P-2PCh-3 P-3PCh-3 P-4PCh-3 P-5PCh-3 P-6PCh-3 P-7PCh-3 P-8PCh-3 P-9PCh-3 P-10PCh-3 P-11PCh-3 P-12PCh-3 P-13PCh-3 P-14PCh-3 P-15PCh-3 P-16PCh-3 P-17PCh-3 P-18PCh-3 P-19PCh-3 P-20PCh-3 P-21PCh-3 P-22PCh-3 P-23PCh-3 P-24PCh-3 P-25PCh-3 P-27PCh-3 P-28PCh-3 P-29PCh-3 P-30PCh-3 P-31PCh-3 P-32PCh-3 P-33PCh-3 P-34PCh-3 P-35P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Evaluate the expression sin Exercises 116. 2322

Finite Mathematics and Applied Calculus (MindTap Course List)

Surface area of a Single-Celled Organism The surface area 5 of a single-celled organism may be found by multipl...

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

Show that ddx arctan(tanh x) = sech 2x.

Single Variable Calculus: Early Transcendentals

True or False: is a geometric series.

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

For f(x, y) = ln(x + y), f(e2, e3) = 2 ln (1 + e) 2 + ln(1 + e) 5

Study Guide for Stewart's Multivariable Calculus, 8th

Self Check Find g-f. Let fx=3x2-5x+1 and gx=2x2+x-3.

College Algebra (MindTap Course List)

Identify the advantages of a multiple-group design compared to an experiment with only two groups.

Research Methods for the Behavioral Sciences (MindTap Course List)