Given that x > 0, find the maximum value, if any, of

Chapter 4, Problem 86E

(choose chapter or problem)

Given that $x>0$, find the maximum value, if any, of

a. $x^{1 / x}$

b. $x^{1 / x^{2}}$

c. $x^{1 / x^{n}}$ ($n$ a positive integer)

d. Show that $\lim _{x \rightarrow \infty} \ x^{1 / x^{n}}=1$ for every positive integer $n$.

Equation Transcription:

x > 0

${x}^{1/x}$

${x}^{1/{x}^{2}}$

${x}^{1/{x}^{n}}$

$li{m}_{x\rightarrow{}\infty{}}\ {x}^{1/{x}^{n}}=1$

Text Transcription:

x > 0

x^1/x

x^1/x^2

x^1/x^n

lim_x right arrow infinity x^1/x^n = 1

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