What is the limit as x approaches 0-of (1/2)^{1/x} ?

The limit as x approaches 0-of (1/2)^{1/x} is infinity

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches 0-of (1/2)^{1/x}

x \to 0 - lim ((\frac{1}{2})^{\frac{1}{x}})

\infty

Solution steps

x \to 0 - lim ((\frac{1}{2})^{\frac{1}{x}})

Apply exponent rule

= x \to 0 - lim (\frac{1}{2 ^{\frac{1}{x}}})

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{2 ^{\frac{1}{x}}} = 2^{- \frac{1}{x}}

= x \to 0 - lim (2^{- \frac{1}{x}})

Apply exponent rules

= x \to 0 - lim (e^{- \frac{1}{x} l n (2)})

Apply the Limit Chain Rule:

\infty

= \infty

What is the limit as x approaches 0-of (1/2)^{1/x} ?
The limit as x approaches 0-of (1/2)^{1/x} is infinity