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

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

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 (1+x/2)^{1/x}

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

e

Decimal

1.64872 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e

= e

\int \frac{x ^{4}}{x ^{3}} d x

\frac{d}{d x} (e^{e x})

x \to + (- \infty) + lim (- 2)

\int \frac{4 - x}{16 - x ^{2}} d x

\frac{d}{d x} (r (h, t, x) i g (h, t, x) h t)

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