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

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

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

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

2 e

Decimal Notation

5.43656 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

2 e

= 2 e

x \to 0 lim (\frac{1 - cos ( 3 x )}{10 x ^{2}})

x \to 0 + lim (\frac{2 + sin ( x )}{x})

x \to 0 - lim (\frac{- 2}{x ^{4}})

x \to 5 lim (\frac{∣ x - 5 ∣}{x + 1})

x \to - 5 + lim (\frac{- 3 x}{x + 5})

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