Chapter 5.6, Problem 113E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Indeterminate Forms Show that the indeterminate forms 0 0 , ∞ 0 , and 1 ∞ do not always have a value of 1 by evaluating each limit.(a) lim x → 0 + x ( ln 2 ) / ( 1 + ln x ) (b) lim x → ∞ x ( ln 2 ) / ( 1 + ln x ) (c) lim x → 0 ( x + 1 ) ( ln 2 ) / x

(a)

To determine

To calculate: The limit of the expression: limx0+x((ln2)(1+lnx)), and verify that it’s not always equal to 1.

Explanation

Given:

The expression is in the form of intermediate form 00, âˆž0 or 1âˆž.

Formula used: Lâ€™ Hospitalâ€™s rule for âˆžâˆž, and direct computation of limit.

Calculation:

The provided expression is: limxâ†’0+x(ln2)(1+lnx).

Itâ€™s in the 00 form.

Let y=limxâ†’0+x(ln2)(1+lnx). â€¦...â€¦...

(b)

To determine

To calculate: The limit of the expression: limx(x)(ln2)(1+lnx), and verify that it’s not always equal to 1.

(c)

To determine

To calculate: The limit of the expression: limx0(x+1)(ln2)(x) and verify that it’s not always equal to 1.

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