Explanation Given info. f ( x ) = ( x ) 1 x , for x > 0 Concept used: x → 0 + , then f ( x ) = ( 0 + ) 1 0 + = ( 0 + ) ∞ = 0 It is not indeterminate form x → ∞ , then f ( x ) Is of the form ( ∞ ) 0 , which is indeterminate form. Tofind lim x → ∞ f ( x ) , convert into appropriate form 0 0 , or ∞ ∞ , then apply L’Hopital’s rule. Calculation: lim x → 0 + f ( x ) lim x → 0 + ( x ) 1 x This limit of the form of ( 0 ) ∞ , which is determinate form, so put the value of limit. = ( 0 + ) 1 0 + = ( 0 + ) ∞ = 0 let lim x → ∞ f ( x ) To determine (b) Let f ( x ) = ( x ) 1 x , for x > 0 Find the maximum value of f and determine the intervals on which f is increasing or decreasing.

Applied Calculus (with Infotrac) 3rd Edition By Waner, Stefan; Costenoble, Steven Published By Brooks Cole Hardcover

3rd Edition

ISBN: 9781319048518

Author: Colin Adams Jon Rogawski

Publisher: Macmillan Higher Education

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Question

Chapter 4.5, Problem 61E

To determine

$\begin{array}{l} Let f (x) = {(x)}^{\frac{1}{x}}, for x > 0 \\ calculate \lim_{x \to 0^{+}} f (x) and \lim_{x \to \infty} f (x) \end{array}$

To determine

(b)

$Let f (x) = {(x)}^{\frac{1}{x},} for x > 0$

Find the maximum value of f and determine the intervals on which f is increasing or decreasing.

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Chapter 4.5, Problem 60E

Chapter 4.5, Problem 62E

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Chapter 4 Solutions

Applied Calculus (with Infotrac) 3rd Edition By Waner, Stefan; Costenoble, Steven Published By Brooks Cole Hardcover

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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Knowledge Booster

Let f ( x ) = ( x ) 1 x , for x &gt; 0 calculate lim x → 0 + f ( x ) and lim x → ∞ f ( x )

Let f(x)=(x)1x, for x>0calculate limx→0+f(x) and limx→∞f(x)

(b) Let f(x)=(x)1x, for x>0 Find the maximum value of f and determine the intervals on which f is increasing or decreasing.

Want to see the full answer?

Chapter 4 Solutions

Let f ( x ) = ( x ) 1 x , for x > 0 calculate lim x → 0 + f ( x ) and lim x → ∞ f ( x )

$\begin{array}{l} Let f (x) = {(x)}^{\frac{1}{x}}, for x > 0 \\ calculate \lim_{x \to 0^{+}} f (x) and \lim_{x \to \infty} f (x) \end{array}$

(b)

$Let f (x) = {(x)}^{\frac{1}{x},} for x > 0$

Find the maximum value of f and determine the intervals on which f is increasing or decreasing.