BuyFindarrow_forward

Single Variable Calculus

8th Edition
James Stewart
ISBN: 9781305266636

Solutions

Chapter
Section
BuyFindarrow_forward

Single Variable Calculus

8th Edition
James Stewart
ISBN: 9781305266636
Textbook Problem

Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain.

29. h(x) = cos(1 − x2)

To determine

To find: The domain and explain the reason for the function to be continuous at every number in the domain.

Explanation

Given:

The function is h(x)=cos(1x2).

Theorems used:

Theorem 4:

If f and g are continuous at a and c is a constant, then the following functions are also continuous at a.

(i) f+g (ii) fg (iii) cf (iv) fg (v) fg if g(a)0.

Theorem 5:

(a) Any polynomial is continuous everywhere; that is, it is continuous on =(,).

(b) Any rational function is continuous wherever it is defined; that is, it is continuous on its domain.

Theorem 7:

The functions such as “Polynomials, rational functions, root functions, trigonometric functions, inverse trigonometric functions, exponential functions and logarithmic functions” are continuous at every number in their domains.

Theorem 9:

If g is continuous at a and f is continuous at g(a), then the composite function fg given by (fg)(x)=f(g(x)) is continuous at a

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-1.1 P-12ESect-1.1 P-13ESect-1.1 P-14ESect-1.1 P-15ESect-1.1 P-16ESect-1.1 P-17ESect-1.1 P-18ESect-1.1 P-19ESect-1.1 P-20ESect-1.1 P-21ESect-1.1 P-22ESect-1.1 P-23ESect-1.1 P-24ESect-1.1 P-25ESect-1.1 P-26ESect-1.1 P-27ESect-1.1 P-28ESect-1.1 P-29ESect-1.1 P-30ESect-1.1 P-31ESect-1.1 P-32ESect-1.1 P-33ESect-1.1 P-34ESect-1.1 P-35ESect-1.1 P-36ESect-1.1 P-37ESect-1.1 P-38ESect-1.1 P-39ESect-1.1 P-40ESect-1.1 P-41ESect-1.1 P-42ESect-1.1 P-43ESect-1.1 P-44ESect-1.1 P-45ESect-1.1 P-46ESect-1.1 P-47ESect-1.1 P-48ESect-1.1 P-49ESect-1.1 P-50ESect-1.1 P-51ESect-1.1 P-52ESect-1.1 P-53ESect-1.1 P-54ESect-1.1 P-55ESect-1.1 P-56ESect-1.1 P-57ESect-1.1 P-58ESect-1.1 P-59ESect-1.1 P-60ESect-1.1 P-61ESect-1.1 P-62ESect-1.1 P-63ESect-1.1 P-64ESect-1.1 P-65ESect-1.1 P-66ESect-1.1 P-67ESect-1.1 P-68ESect-1.1 P-69ESect-1.1 P-70ESect-1.1 P-71ESect-1.1 P-72ESect-1.1 P-73ESect-1.1 P-74ESect-1.1 P-75ESect-1.1 P-76ESect-1.1 P-77ESect-1.1 P-78ESect-1.1 P-79ESect-1.1 P-80ESect-1.2 P-1ESect-1.2 P-2ESect-1.2 P-3ESect-1.2 P-4ESect-1.2 P-5ESect-1.2 P-6ESect-1.2 P-7ESect-1.2 P-8ESect-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-1.3 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-10ESect-1.3 P-11ESect-1.3 P-12ESect-1.3 P-13ESect-1.3 P-14ESect-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-41ESect-1.3 P-42ESect-1.3 P-43ESect-1.3 P-44ESect-1.3 P-45ESect-1.3 P-46ESect-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-1.4 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-1.5 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-1.6 P-1ESect-1.6 P-2ESect-1.6 P-3ESect-1.6 P-4ESect-1.6 P-5ESect-1.6 P-6ESect-1.6 P-7ESect-1.6 P-8ESect-1.6 P-9ESect-1.6 P-10ESect-1.6 P-11ESect-1.6 P-12ESect-1.6 P-13ESect-1.6 P-14ESect-1.6 P-15ESect-1.6 P-16ESect-1.6 P-17ESect-1.6 P-18ESect-1.6 P-19ESect-1.6 P-20ESect-1.6 P-21ESect-1.6 P-22ESect-1.6 P-23ESect-1.6 P-24ESect-1.6 P-25ESect-1.6 P-26ESect-1.6 P-27ESect-1.6 P-28ESect-1.6 P-29ESect-1.6 P-30ESect-1.6 P-31ESect-1.6 P-32ESect-1.6 P-33ESect-1.6 P-34ESect-1.6 P-35ESect-1.6 P-36ESect-1.6 P-37ESect-1.6 P-38ESect-1.6 P-39ESect-1.6 P-40ESect-1.6 P-41ESect-1.6 P-42ESect-1.6 P-43ESect-1.6 P-44ESect-1.6 P-45ESect-1.6 P-46ESect-1.6 P-47ESect-1.6 P-48ESect-1.6 P-49ESect-1.6 P-50ESect-1.6 P-51ESect-1.6 P-52ESect-1.6 P-53ESect-1.6 P-54ESect-1.6 P-55ESect-1.6 P-56ESect-1.6 P-57ESect-1.6 P-58ESect-1.6 P-59ESect-1.6 P-60ESect-1.6 P-61ESect-1.6 P-62ESect-1.6 P-63ESect-1.6 P-64ESect-1.6 P-65ESect-1.6 P-66ESect-1.7 P-1ESect-1.7 P-2ESect-1.7 P-3ESect-1.7 P-4ESect-1.7 P-5ESect-1.7 P-6ESect-1.7 P-7ESect-1.7 P-8ESect-1.7 P-9ESect-1.7 P-10ESect-1.7 P-11ESect-1.7 P-12ESect-1.7 P-13ESect-1.7 P-14ESect-1.7 P-15ESect-1.7 P-16ESect-1.7 P-17ESect-1.7 P-18ESect-1.7 P-19ESect-1.7 P-20ESect-1.7 P-21ESect-1.7 P-22ESect-1.7 P-23ESect-1.7 P-24ESect-1.7 P-25ESect-1.7 P-26ESect-1.7 P-27ESect-1.7 P-28ESect-1.7 P-29ESect-1.7 P-30ESect-1.7 P-31ESect-1.7 P-32ESect-1.7 P-33ESect-1.7 P-34ESect-1.7 P-36ESect-1.7 P-37ESect-1.7 P-38ESect-1.7 P-39ESect-1.7 P-40ESect-1.7 P-41ESect-1.7 P-42ESect-1.7 P-43ESect-1.7 P-44ESect-1.8 P-1ESect-1.8 P-2ESect-1.8 P-3ESect-1.8 P-4ESect-1.8 P-5ESect-1.8 P-6ESect-1.8 P-7ESect-1.8 P-8ESect-1.8 P-9ESect-1.8 P-10ESect-1.8 P-11ESect-1.8 P-12ESect-1.8 P-13ESect-1.8 P-14ESect-1.8 P-15ESect-1.8 P-16ESect-1.8 P-17ESect-1.8 P-18ESect-1.8 P-19ESect-1.8 P-20ESect-1.8 P-21ESect-1.8 P-22ESect-1.8 P-23ESect-1.8 P-24ESect-1.8 P-25ESect-1.8 P-26ESect-1.8 P-27ESect-1.8 P-28ESect-1.8 P-29ESect-1.8 P-30ESect-1.8 P-31ESect-1.8 P-32ESect-1.8 P-33ESect-1.8 P-34ESect-1.8 P-35ESect-1.8 P-36ESect-1.8 P-37ESect-1.8 P-38ESect-1.8 P-39ESect-1.8 P-40ESect-1.8 P-41ESect-1.8 P-42ESect-1.8 P-43ESect-1.8 P-44ESect-1.8 P-45ESect-1.8 P-46ESect-1.8 P-47ESect-1.8 P-48ESect-1.8 P-49ESect-1.8 P-50ESect-1.8 P-51ESect-1.8 P-52ESect-1.8 P-53ESect-1.8 P-54ESect-1.8 P-55ESect-1.8 P-56ESect-1.8 P-57ESect-1.8 P-58ESect-1.8 P-59ESect-1.8 P-60ESect-1.8 P-61ESect-1.8 P-62ESect-1.8 P-63ESect-1.8 P-64ESect-1.8 P-65ESect-1.8 P-66ESect-1.8 P-67ESect-1.8 P-68ESect-1.8 P-69ESect-1.8 P-70ESect-1.8 P-71ESect-1.8 P-72ESect-1.8 P-73ECh-1 P-1RCCCh-1 P-2RCCCh-1 P-3RCCCh-1 P-4RCCCh-1 P-5RCCCh-1 P-6RCCCh-1 P-7RCCCh-1 P-8RCCCh-1 P-9RCCCh-1 P-10RCCCh-1 P-11RCCCh-1 P-12RCCCh-1 P-13RCCCh-1 P-14RCCCh-1 P-15RCCCh-1 P-16RCCCh-1 P-17RCCCh-1 P-18RCCCh-1 P-19RCCCh-1 P-1RQCh-1 P-2RQCh-1 P-3RQCh-1 P-4RQCh-1 P-5RQCh-1 P-6RQCh-1 P-7RQCh-1 P-8RQCh-1 P-9RQCh-1 P-10RQCh-1 P-11RQCh-1 P-12RQCh-1 P-13RQCh-1 P-14RQCh-1 P-15RQCh-1 P-16RQCh-1 P-17RQCh-1 P-18RQCh-1 P-19RQCh-1 P-20RQCh-1 P-21RQCh-1 P-22RQCh-1 P-23RQCh-1 P-24RQCh-1 P-25RQCh-1 P-26RQCh-1 P-27RQCh-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-14RECh-1 P-15RECh-1 P-16RECh-1 P-17RECh-1 P-18RECh-1 P-19RECh-1 P-20RECh-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-1PCh-1 P-2PCh-1 P-3PCh-1 P-4PCh-1 P-5PCh-1 P-6PCh-1 P-7PCh-1 P-8PCh-1 P-9PCh-1 P-10PCh-1 P-11PCh-1 P-12PCh-1 P-13PCh-1 P-14PCh-1 P-15PCh-1 P-16PCh-1 P-17PCh-1 P-18PCh-1 P-19PCh-1 P-20PCh-1 P-21PCh-1 P-22PCh-1 P-23PCh-1 P-24PCh-1 P-25P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Keeping with the Traffic Flow By driving at a speed to match the prevailing traffic speed, you decrease the cha...

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

Evaluate the integral. 6. 01x(2x+1)3dx

Calculus: Early Transcendentals

Find the differential of the function. R=2cos

Calculus (MindTap Course List)

Use the matrices below a needed to complete Problems 1-25, Find in matrix .

Mathematical Applications for the Management, Life, and Social Sciences

What is a random variable? Give an example.

Finite Mathematics for the Managerial, Life, and Social Sciences