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

Use the guidelines of this section to sketch the curve.

y = ln(sin x)

To determine

To Find: The curve by plotting x and y coordinates using guideline.

Explanation

Given:

The given curve is as below.

f(x)=y=lnsinx (1)

Calculation:

(a)

Calculate the domain.

The function f(x) is undefined for sinx=0 .

Therefore, the domain is x(2nπ,π+2nπ) .

(b)

Calculate the intercepts.

Calculate the y intercept.

Substitute 0 for the value of x in equation (1).

f(x)=lnsinx

f(0)=lnsin0=ln0=

The y intercept does not exist.

Calculate the value of x intercept.

Substitute 0 for y in the equation (1).

lnsinx=0

Here the term ln(1)=0 .

So sinx=1

Therefore, x intercept occurs when the condition x=π2+2nπ is true.

(c)

Calculate the symmetry.

Substitute x for x in the equation (1).

f(x)=lnsin(x)f(x)f(x)

The function is neither even nor odd. Therefore, the curve is not symmetric about y axis and origin.

(d)

Calculate asymptotes.

Apply limit of x tends to nπ (xnπ) in the equation (1).

limxnπf(x)=lnsin(nπ)=lnsin(nπ)=

It has the vertical asymptotes x=nπ . Horizontal asymptotes do not exist.

(e)

Calculate the intervals.

f(x)=lnsinx

Differentiate the equation (1) with respect to x .

f'(x)=dln(sinx)dsinx×dsinxdx=d(sinx)sinx

f'(x)=cotx (2)

So equate equation (2) to zero.

cotx=0x=cot1(0)=π2+nπ

Consider the limit (0,π)

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-4.1 P-33ESect-4.1 P-34ESect-4.1 P-35ESect-4.1 P-36ESect-4.1 P-37ESect-4.1 P-38ESect-4.1 P-39ESect-4.1 P-40ESect-4.1 P-41ESect-4.1 P-42ESect-4.1 P-43ESect-4.1 P-44ESect-4.1 P-45ESect-4.1 P-46ESect-4.1 P-47ESect-4.1 P-48ESect-4.1 P-49ESect-4.1 P-50ESect-4.1 P-51ESect-4.1 P-52ESect-4.1 P-53ESect-4.1 P-54ESect-4.1 P-55ESect-4.1 P-56ESect-4.1 P-57ESect-4.1 P-58ESect-4.1 P-59ESect-4.1 P-60ESect-4.1 P-61ESect-4.1 P-62ESect-4.1 P-63ESect-4.1 P-64ESect-4.1 P-65ESect-4.1 P-66ESect-4.1 P-67ESect-4.1 P-68ESect-4.1 P-69ESect-4.1 P-70ESect-4.1 P-71ESect-4.1 P-72ESect-4.1 P-73ESect-4.1 P-74ESect-4.1 P-75ESect-4.1 P-76ESect-4.1 P-77ESect-4.1 P-78ESect-4.1 P-79ESect-4.1 P-80ESect-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-36ESect-4.2 P-37ESect-4.2 P-38ESect-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-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-4.3 P-85ESect-4.3 P-86ESect-4.3 P-87ESect-4.3 P-88ESect-4.3 P-89ESect-4.3 P-90ESect-4.3 P-92ESect-4.3 P-93ESect-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-4.4 P-75ESect-4.4 P-76ESect-4.4 P-77ESect-4.4 P-78ESect-4.4 P-79ESect-4.4 P-80ESect-4.4 P-81ESect-4.4 P-82ESect-4.4 P-83ESect-4.4 P-84ESect-4.4 P-85ESect-4.4 P-86ESect-4.4 P-87ESect-4.4 P-88ESect-4.4 P-89ESect-4.4 P-90ESect-4.4 P-91ESect-4.4 P-92ESect-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-4.6 P-1ESect-4.6 P-2ESect-4.6 P-3ESect-4.6 P-4ESect-4.6 P-5ESect-4.6 P-6ESect-4.6 P-9ESect-4.6 P-10ESect-4.6 P-13ESect-4.6 P-14ESect-4.6 P-27ESect-4.6 P-28ESect-4.6 P-29ESect-4.6 P-30ESect-4.6 P-33ESect-4.6 P-34ESect-4.6 P-35ESect-4.6 P-38ESect-4.6 P-39ESect-4.6 P-40ESect-4.7 P-1ESect-4.7 P-2ESect-4.7 P-3ESect-4.7 P-4ESect-4.7 P-5ESect-4.7 P-6ESect-4.7 P-7ESect-4.7 P-8ESect-4.7 P-9ESect-4.7 P-10ESect-4.7 P-11ESect-4.7 P-12ESect-4.7 P-13ESect-4.7 P-14ESect-4.7 P-15ESect-4.7 P-16ESect-4.7 P-17ESect-4.7 P-18ESect-4.7 P-19ESect-4.7 P-20ESect-4.7 P-21ESect-4.7 P-22ESect-4.7 P-23ESect-4.7 P-24ESect-4.7 P-25ESect-4.7 P-26ESect-4.7 P-27ESect-4.7 P-28ESect-4.7 P-29ESect-4.7 P-30ESect-4.7 P-31ESect-4.7 P-32ESect-4.7 P-33ESect-4.7 P-34ESect-4.7 P-35ESect-4.7 P-36ESect-4.7 P-37ESect-4.7 P-38ESect-4.7 P-39ESect-4.7 P-40ESect-4.7 P-41ESect-4.7 P-42ESect-4.7 P-43ESect-4.7 P-44ESect-4.7 P-45ESect-4.7 P-46ESect-4.7 P-47ESect-4.7 P-48ESect-4.7 P-49ESect-4.7 P-50ESect-4.7 P-51ESect-4.7 P-52ESect-4.7 P-53ESect-4.7 P-54ESect-4.7 P-55ESect-4.7 P-56ESect-4.7 P-57ESect-4.7 P-58ESect-4.7 P-59ESect-4.7 P-60ESect-4.7 P-61ESect-4.7 P-62ESect-4.7 P-63ESect-4.7 P-64ESect-4.7 P-65ESect-4.7 P-66ESect-4.7 P-67ESect-4.7 P-68ESect-4.7 P-69ESect-4.7 P-70ESect-4.7 P-71ESect-4.7 P-72ESect-4.7 P-73ESect-4.7 P-74ESect-4.7 P-75ESect-4.7 P-76ESect-4.7 P-77ESect-4.7 P-78ESect-4.7 P-79ESect-4.7 P-80ESect-4.7 P-81ESect-4.7 P-82ESect-4.8 P-1ESect-4.8 P-2ESect-4.8 P-3ESect-4.8 P-4ESect-4.8 P-5ESect-4.8 P-6ESect-4.8 P-7ESect-4.8 P-8ESect-4.8 P-9ESect-4.8 P-10ESect-4.8 P-11ESect-4.8 P-12ESect-4.8 P-13ESect-4.8 P-14ESect-4.8 P-15ESect-4.8 P-16ESect-4.8 P-17ESect-4.8 P-18ESect-4.8 P-19ESect-4.8 P-20ESect-4.8 P-21ESect-4.8 P-22ESect-4.8 P-23ESect-4.8 P-24ESect-4.8 P-25ESect-4.8 P-26ESect-4.8 P-27ESect-4.8 P-29ESect-4.8 P-30ESect-4.8 P-32ESect-4.8 P-33ESect-4.8 P-34ESect-4.8 P-35ESect-4.8 P-36ESect-4.8 P-37ESect-4.8 P-39ESect-4.8 P-40ESect-4.8 P-41ESect-4.8 P-42ESect-4.9 P-1ESect-4.9 P-2ESect-4.9 P-3ESect-4.9 P-4ESect-4.9 P-5ESect-4.9 P-6ESect-4.9 P-7ESect-4.9 P-8ESect-4.9 P-9ESect-4.9 P-10ESect-4.9 P-11ESect-4.9 P-12ESect-4.9 P-13ESect-4.9 P-14ESect-4.9 P-15ESect-4.9 P-16ESect-4.9 P-17ESect-4.9 P-18ESect-4.9 P-19ESect-4.9 P-20ESect-4.9 P-21ESect-4.9 P-22ESect-4.9 P-25ESect-4.9 P-26ESect-4.9 P-27ESect-4.9 P-28ESect-4.9 P-29ESect-4.9 P-30ESect-4.9 P-31ESect-4.9 P-32ESect-4.9 P-33ESect-4.9 P-34ESect-4.9 P-35ESect-4.9 P-36ESect-4.9 P-37ESect-4.9 P-38ESect-4.9 P-39ESect-4.9 P-40ESect-4.9 P-41ESect-4.9 P-42ESect-4.9 P-43ESect-4.9 P-44ESect-4.9 P-45ESect-4.9 P-46ESect-4.9 P-47ESect-4.9 P-48ESect-4.9 P-49ESect-4.9 P-50ESect-4.9 P-51ESect-4.9 P-52ESect-4.9 P-53ESect-4.9 P-54ESect-4.9 P-55ESect-4.9 P-56ESect-4.9 P-57ESect-4.9 P-58ESect-4.9 P-59ESect-4.9 P-60ESect-4.9 P-61ESect-4.9 P-62ESect-4.9 P-63ESect-4.9 P-64ESect-4.9 P-65ESect-4.9 P-66ESect-4.9 P-67ESect-4.9 P-68ESect-4.9 P-69ESect-4.9 P-70ESect-4.9 P-71ESect-4.9 P-72ESect-4.9 P-73ESect-4.9 P-74ESect-4.9 P-75ESect-4.9 P-76ESect-4.9 P-77ESect-4.9 P-79ECh-4 P-1RCCCh-4 P-2RCCCh-4 P-3RCCCh-4 P-4RCCCh-4 P-5RCCCh-4 P-6RCCCh-4 P-7RCCCh-4 P-8RCCCh-4 P-9RCCCh-4 P-10RCCCh-4 P-11RCCCh-4 P-1RQCh-4 P-2RQCh-4 P-3RQCh-4 P-4RQCh-4 P-5RQCh-4 P-6RQCh-4 P-7RQCh-4 P-8RQCh-4 P-9RQCh-4 P-10RQCh-4 P-11RQCh-4 P-12RQCh-4 P-13RQCh-4 P-14RQCh-4 P-15RQCh-4 P-16RQCh-4 P-17RQCh-4 P-18RQCh-4 P-19RQCh-4 P-20RQCh-4 P-21RQCh-4 P-1RECh-4 P-2RECh-4 P-3RECh-4 P-4RECh-4 P-5RECh-4 P-6RECh-4 P-7RECh-4 P-8RECh-4 P-9RECh-4 P-10RECh-4 P-11RECh-4 P-12RECh-4 P-13RECh-4 P-14RECh-4 P-15RECh-4 P-16RECh-4 P-17RECh-4 P-18RECh-4 P-19RECh-4 P-20RECh-4 P-21RECh-4 P-22RECh-4 P-23RECh-4 P-24RECh-4 P-25RECh-4 P-26RECh-4 P-27RECh-4 P-28RECh-4 P-29RECh-4 P-30RECh-4 P-31RECh-4 P-32RECh-4 P-33RECh-4 P-34RECh-4 P-35RECh-4 P-36RECh-4 P-37RECh-4 P-38RECh-4 P-39RECh-4 P-43RECh-4 P-44RECh-4 P-45RECh-4 P-46RECh-4 P-47RECh-4 P-48RECh-4 P-49RECh-4 P-50RECh-4 P-51RECh-4 P-52RECh-4 P-53RECh-4 P-54RECh-4 P-55RECh-4 P-56RECh-4 P-57RECh-4 P-58RECh-4 P-59RECh-4 P-60RECh-4 P-61RECh-4 P-62RECh-4 P-63RECh-4 P-64RECh-4 P-65RECh-4 P-66RECh-4 P-67RECh-4 P-68RECh-4 P-69RECh-4 P-70RECh-4 P-71RECh-4 P-72RECh-4 P-73RECh-4 P-74RECh-4 P-75RECh-4 P-76RECh-4 P-77RECh-4 P-78RECh-4 P-79RECh-4 P-80RECh-4 P-81RECh-4 P-82RECh-4 P-83RECh-4 P-84RECh-4 P-85RECh-4 P-86RECh-4 P-1PCh-4 P-2PCh-4 P-3PCh-4 P-4PCh-4 P-5PCh-4 P-6PCh-4 P-7PCh-4 P-8PCh-4 P-9PCh-4 P-10PCh-4 P-11PCh-4 P-12PCh-4 P-13PCh-4 P-14PCh-4 P-15PCh-4 P-16PCh-4 P-17PCh-4 P-18PCh-4 P-19PCh-4 P-20PCh-4 P-21PCh-4 P-22PCh-4 P-23PCh-4 P-25PCh-4 P-26P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

In Exercises 516, evaluate the given quantity. log218

Finite Mathematics and Applied Calculus (MindTap Course List)

Factoring Completely Factor the expression completely. 116. x6 + 64

Precalculus: Mathematics for Calculus (Standalone Book)

In Exercises 47-52, find and simplify f(a+h)f(a)h(h0) for each function. 51. f(x)=1x

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

In problems 7-12, evaluate each algebraic expression at the indicated values of the variables. 12. at

Mathematical Applications for the Management, Life, and Social Sciences

Perform the indicated operations: 28+(11)

Elementary Technical Mathematics

True or False: is a convergent series.

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

True or False: converges.

Study Guide for Stewart's Multivariable Calculus, 8th