BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Proof Prove Property 1 of Theorem 1.2.

To determine

To prove: limxcbf(x)=bL, where b and c are real numbers.

Explanation

Given:

The limit,

limxcf(x)=L

Formula used:

If there exists a limit limxaf(x)=b, then for given >0 there must be a δ>0 such that,

|f(x)b|<ε|b| for the interval 0<|xa|<δ.

Proof:

If b=0, then,

limxcbf(x)=bL0=0

Thus, the property holds true for b=0.

Now, if b0, then,

Consider ε>0

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-1.1 P-11ESect-1.2 P-1ESect-1.2 P-2ESect-1.2 P-3ESect-1.2 P-4ESect-1.2 P-5ESect-1.2 P-7ESect-1.2 P-9ESect-1.2 P-10ESect-1.2 P-11ESect-1.2 P-12ESect-1.2 P-13ESect-1.2 P-14ESect-1.2 P-15ESect-1.2 P-16ESect-1.2 P-17ESect-1.2 P-18ESect-1.2 P-19ESect-1.2 P-20ESect-1.2 P-21ESect-1.2 P-22ESect-1.2 P-23ESect-1.2 P-24ESect-1.2 P-25ESect-1.2 P-26ESect-1.2 P-27ESect-1.2 P-28ESect-1.2 P-29ESect-1.2 P-30ESect-1.2 P-31ESect-1.2 P-32ESect-1.2 P-33ESect-1.2 P-34ESect-1.2 P-35ESect-1.2 P-36ESect-1.2 P-37ESect-1.2 P-38ESect-1.2 P-39ESect-1.2 P-40ESect-1.2 P-41ESect-1.2 P-42ESect-1.2 P-43ESect-1.2 P-44ESect-1.2 P-45ESect-1.2 P-46ESect-1.2 P-47ESect-1.2 P-48ESect-1.2 P-49ESect-1.2 P-50ESect-1.2 P-51ESect-1.2 P-52ESect-1.2 P-53ESect-1.2 P-54ESect-1.2 P-55ESect-1.2 P-56ESect-1.2 P-57ESect-1.2 P-58ESect-1.2 P-59ESect-1.2 P-60ESect-1.2 P-61ESect-1.2 P-62ESect-1.2 P-63ESect-1.2 P-64ESect-1.2 P-65ESect-1.2 P-66ESect-1.2 P-67ESect-1.2 P-68ESect-1.2 P-69ESect-1.2 P-70ESect-1.2 P-71ESect-1.2 P-72ESect-1.2 P-73ESect-1.2 P-74ESect-1.2 P-75ESect-1.2 P-76ESect-1.2 P-77ESect-1.2 P-78ESect-1.2 P-79ESect-1.2 P-80ESect-1.2 P-81ESect-1.2 P-82ESect-1.2 P-83ESect-1.2 P-84ESect-1.2 P-85ESect-1.2 P-86ESect-1.2 P-6ESect-1.2 P-8ESect-1.3 P-1ESect-1.3 P-2ESect-1.3 P-3ESect-1.3 P-4ESect-1.3 P-5ESect-1.3 P-6ESect-1.3 P-7ESect-1.3 P-8ESect-1.3 P-9ESect-1.3 P-12ESect-1.3 P-13ESect-1.3 P-14ESect-1.3 P-11ESect-1.3 P-10ESect-1.3 P-15ESect-1.3 P-16ESect-1.3 P-17ESect-1.3 P-18ESect-1.3 P-19ESect-1.3 P-20ESect-1.3 P-21ESect-1.3 P-22ESect-1.3 P-23ESect-1.3 P-24ESect-1.3 P-25ESect-1.3 P-26ESect-1.3 P-27ESect-1.3 P-28ESect-1.3 P-29ESect-1.3 P-30ESect-1.3 P-31ESect-1.3 P-32ESect-1.3 P-33ESect-1.3 P-34ESect-1.3 P-35ESect-1.3 P-36ESect-1.3 P-37ESect-1.3 P-38ESect-1.3 P-39ESect-1.3 P-40ESect-1.3 P-43ESect-1.3 P-44ESect-1.3 P-45ESect-1.3 P-46ESect-1.3 P-41ESect-1.3 P-42ESect-1.3 P-47ESect-1.3 P-48ESect-1.3 P-49ESect-1.3 P-50ESect-1.3 P-51ESect-1.3 P-52ESect-1.3 P-53ESect-1.3 P-54ESect-1.3 P-55ESect-1.3 P-56ESect-1.3 P-57ESect-1.3 P-58ESect-1.3 P-59ESect-1.3 P-60ESect-1.3 P-61ESect-1.3 P-62ESect-1.3 P-63ESect-1.3 P-64ESect-1.3 P-65ESect-1.3 P-66ESect-1.3 P-67ESect-1.3 P-68ESect-1.3 P-69ESect-1.3 P-70ESect-1.3 P-71ESect-1.3 P-72ESect-1.3 P-73ESect-1.3 P-74ESect-1.3 P-75ESect-1.3 P-76ESect-1.3 P-77ESect-1.3 P-78ESect-1.3 P-79ESect-1.3 P-80ESect-1.3 P-81ESect-1.3 P-82ESect-1.3 P-83ESect-1.3 P-84ESect-1.3 P-85ESect-1.3 P-86ESect-1.3 P-87ESect-1.3 P-88ESect-1.3 P-89ESect-1.3 P-90ESect-1.3 P-91ESect-1.3 P-92ESect-1.3 P-93ESect-1.3 P-94ESect-1.3 P-95ESect-1.3 P-96ESect-1.3 P-97ESect-1.3 P-98ESect-1.3 P-99ESect-1.3 P-100ESect-1.3 P-101ESect-1.3 P-102ESect-1.3 P-103ESect-1.3 P-104ESect-1.3 P-105ESect-1.3 P-106ESect-1.3 P-107ESect-1.3 P-108ESect-1.3 P-109ESect-1.3 P-110ESect-1.3 P-111ESect-1.3 P-112ESect-1.3 P-113ESect-1.3 P-114ESect-1.3 P-115ESect-1.3 P-116ESect-1.3 P-117ESect-1.3 P-118ESect-1.3 P-119ESect-1.3 P-120ESect-1.3 P-121ESect-1.3 P-122ESect-1.3 P-123ESect-1.3 P-124ESect-1.4 P-1ESect-1.4 P-2ESect-1.4 P-3ESect-1.4 P-4ESect-1.4 P-5ESect-1.4 P-6ESect-1.4 P-7ESect-1.4 P-8ESect-1.4 P-9ESect-1.4 P-10ESect-1.4 P-11ESect-1.4 P-12ESect-1.4 P-13ESect-1.4 P-14ESect-1.4 P-15ESect-1.4 P-16ESect-1.4 P-17ESect-1.4 P-18ESect-1.4 P-19ESect-1.4 P-20ESect-1.4 P-21ESect-1.4 P-22ESect-1.4 P-23ESect-1.4 P-24ESect-1.4 P-25ESect-1.4 P-26ESect-1.4 P-27ESect-1.4 P-28ESect-1.4 P-29ESect-1.4 P-30ESect-1.4 P-31ESect-1.4 P-32ESect-1.4 P-33ESect-1.4 P-34ESect-1.4 P-35ESect-1.4 P-36ESect-1.4 P-37ESect-1.4 P-38ESect-1.4 P-39ESect-1.4 P-40ESect-1.4 P-41ESect-1.4 P-42ESect-1.4 P-43ESect-1.4 P-44ESect-1.4 P-45ESect-1.4 P-46ESect-1.4 P-47ESect-1.4 P-48ESect-1.4 P-49ESect-1.4 P-50ESect-1.4 P-51ESect-1.4 P-52ESect-1.4 P-53ESect-1.4 P-54ESect-1.4 P-55ESect-1.4 P-56ESect-1.4 P-57ESect-1.4 P-58ESect-1.4 P-59ESect-1.4 P-60ESect-1.4 P-61ESect-1.4 P-62ESect-1.4 P-63ESect-1.4 P-64ESect-1.4 P-65ESect-1.4 P-66ESect-1.4 P-67ESect-1.4 P-68ESect-1.4 P-69ESect-1.4 P-70ESect-1.4 P-71ESect-1.4 P-72ESect-1.4 P-73ESect-1.4 P-74ESect-1.4 P-75ESect-1.4 P-76ESect-1.4 P-77ESect-1.4 P-78ESect-1.4 P-79ESect-1.4 P-80ESect-1.4 P-81ESect-1.4 P-82ESect-1.4 P-83ESect-1.4 P-84ESect-1.4 P-85ESect-1.4 P-86ESect-1.4 P-87ESect-1.4 P-88ESect-1.4 P-89ESect-1.4 P-90ESect-1.4 P-91ESect-1.4 P-92ESect-1.4 P-93ESect-1.4 P-94ESect-1.4 P-95ESect-1.4 P-96ESect-1.4 P-97ESect-1.4 P-98ESect-1.4 P-99ESect-1.4 P-100ESect-1.4 P-101ESect-1.4 P-102ESect-1.4 P-103ESect-1.4 P-104ESect-1.4 P-105ESect-1.4 P-106ESect-1.4 P-107ESect-1.4 P-108ESect-1.4 P-109ESect-1.4 P-110ESect-1.4 P-111ESect-1.4 P-112ESect-1.4 P-113ESect-1.4 P-114ESect-1.4 P-115ESect-1.4 P-116ESect-1.4 P-117ESect-1.4 P-118ESect-1.4 P-119ESect-1.4 P-120ESect-1.4 P-121ESect-1.4 P-122ESect-1.4 P-123ESect-1.4 P-124ESect-1.4 P-125ESect-1.4 P-126ESect-1.4 P-127ESect-1.4 P-128ESect-1.4 P-129ESect-1.4 P-130ESect-1.5 P-1ESect-1.5 P-2ESect-1.5 P-3ESect-1.5 P-4ESect-1.5 P-5ESect-1.5 P-6ESect-1.5 P-7ESect-1.5 P-8ESect-1.5 P-9ESect-1.5 P-10ESect-1.5 P-11ESect-1.5 P-12ESect-1.5 P-13ESect-1.5 P-14ESect-1.5 P-15ESect-1.5 P-16ESect-1.5 P-17ESect-1.5 P-18ESect-1.5 P-19ESect-1.5 P-20ESect-1.5 P-21ESect-1.5 P-22ESect-1.5 P-23ESect-1.5 P-24ESect-1.5 P-25ESect-1.5 P-26ESect-1.5 P-27ESect-1.5 P-28ESect-1.5 P-29ESect-1.5 P-30ESect-1.5 P-31ESect-1.5 P-32ESect-1.5 P-33ESect-1.5 P-34ESect-1.5 P-35ESect-1.5 P-36ESect-1.5 P-37ESect-1.5 P-38ESect-1.5 P-39ESect-1.5 P-40ESect-1.5 P-41ESect-1.5 P-42ESect-1.5 P-43ESect-1.5 P-44ESect-1.5 P-45ESect-1.5 P-46ESect-1.5 P-47ESect-1.5 P-48ESect-1.5 P-49ESect-1.5 P-50ESect-1.5 P-51ESect-1.5 P-52ESect-1.5 P-53ESect-1.5 P-54ESect-1.5 P-55ESect-1.5 P-56ESect-1.5 P-57ESect-1.5 P-58ESect-1.5 P-59ESect-1.5 P-60ESect-1.5 P-61ESect-1.5 P-62ESect-1.5 P-63ESect-1.5 P-64ESect-1.5 P-65ESect-1.5 P-66ESect-1.5 P-67ESect-1.5 P-68ESect-1.5 P-69ESect-1.5 P-70ESect-1.5 P-71ESect-1.5 P-72ESect-1.5 P-73ESect-1.5 P-74ESect-1.5 P-75ESect-1.5 P-76ECh-1 P-1RECh-1 P-2RECh-1 P-3RECh-1 P-4RECh-1 P-5RECh-1 P-6RECh-1 P-7RECh-1 P-8RECh-1 P-9RECh-1 P-10RECh-1 P-11RECh-1 P-12RECh-1 P-13RECh-1 P-15RECh-1 P-14RECh-1 P-16RECh-1 P-17RECh-1 P-18RECh-1 P-19RECh-1 P-20RECh-1 P-21RECh-1 P-22RECh-1 P-23RECh-1 P-24RECh-1 P-25RECh-1 P-26RECh-1 P-27RECh-1 P-28RECh-1 P-29RECh-1 P-30RECh-1 P-31RECh-1 P-32RECh-1 P-33RECh-1 P-34RECh-1 P-35RECh-1 P-36RECh-1 P-37RECh-1 P-38RECh-1 P-39RECh-1 P-40RECh-1 P-41RECh-1 P-42RECh-1 P-43RECh-1 P-44RECh-1 P-45RECh-1 P-46RECh-1 P-47RECh-1 P-48RECh-1 P-49RECh-1 P-50RECh-1 P-51RECh-1 P-52RECh-1 P-53RECh-1 P-54RECh-1 P-55RECh-1 P-56RECh-1 P-57RECh-1 P-58RECh-1 P-59RECh-1 P-60RECh-1 P-61RECh-1 P-62RECh-1 P-63RECh-1 P-64RECh-1 P-65RECh-1 P-66RECh-1 P-67RECh-1 P-68RECh-1 P-69RECh-1 P-70RECh-1 P-71RECh-1 P-72RECh-1 P-73RECh-1 P-74RECh-1 P-75RECh-1 P-76RECh-1 P-77RECh-1 P-78RECh-1 P-79RECh-1 P-80RECh-1 P-81RECh-1 P-82RECh-1 P-83RECh-1 P-84RECh-1 P-85RECh-1 P-86RECh-1 P-87RECh-1 P-88RECh-1 P-89RECh-1 P-1PSCh-1 P-2PSCh-1 P-3PSCh-1 P-4PSCh-1 P-5PSCh-1 P-6PSCh-1 P-7PSCh-1 P-8PSCh-1 P-9PSCh-1 P-10PSCh-1 P-11PSCh-1 P-12PSCh-1 P-13PSCh-1 P-14PS

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Solve the equations in Exercises 112 for x (mentally, if possible). 3x+1=x

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 7-12, refer to the following figure. 8. What are the coordinates of point B?

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

Change 7200 ft/min to ft/s.

Elementary Technical Mathematics

The populations of sheep and wolves on an island is governed by a predator-prey model with constants k = 0.03, ...

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

Write in cylindrical coordinates, where E is the solid at the right.

Study Guide for Stewart's Multivariable Calculus, 8th