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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

- \infty

Solution steps

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

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

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

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

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

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

= 1 \cdot (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

\frac{d}{d x} (\frac{x ^{3}}{100} - \frac{1500}{x})

\int 11 arctan (x) d x

\frac{d}{d x} (16 in (x^{2}) - x^{2})

f (x) = \frac{1}{x - 1}, at x = 3

\int e^{2 x - 1} d x

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