   Chapter 4.3, Problem 55E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# (a) Find the vertical and horizontal asymptotes.(b) Find the intervals of increase or decrease.(c) Find the local maximum and minimum values.(d) Find the intervals of concavity and the inflection points.(e) Use the information from parts (a)−(d) to sketch the graph of f.f(x) = ln(1 − ln x)

(a)

To determine

To find: The vertical and horizontal asymptotes of the function f(x)=ln(1lnx) .

Explanation

Calculation:

Vertical asymptote is obtain at x=a , if limxaf(x)= or limxaf(x)= .

As x approaches 0,

limx0f(x)=limx0ln(1lnx)=ln(1limx0lnx)=ln(1)=

As x approaches e,

limxef(x)=limxeln(1lnx)=ln(1limxelnx)=ln(1lne)=ln(11)

Simplify further to check the vertical asymptote at x=e .

limxef(x)=ln(0)=

Hence, the function is undefined when x=0 and x=e

(b)

To determine

To find: On which intervals the function f(x)=ln(1lnx) is increasing or decreasing.

(c)

To determine

To find: The local maximum and minimum values of the function f(x)=ln(1lnx) .

(d)

To determine

To find: The intervals of concavity and the inflection points of the function f(x)=ln(1lnx) .

(e)

To determine

To sketch: The graph of the function for the above information from part (a) to part (d).

### 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

#### Place the following set of n = 20 scores in a frequency distribution table.

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### Sum of Square (SS), variance and standard deviation

Statistics for The Behavioral Sciences (MindTap Course List)

#### In Exercises 69-74, rationalize the numerator. 71. 2yx

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

#### Calculate y'. 18. y = cot(csc x)

Single Variable Calculus: Early Transcendentals

#### The appropriate option for the value of the indefinite integral ∫sinx2 dx.

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