What is the limit as x approaches 0 of (e^x+x)^{3/x} ?

The limit as x approaches 0 of (e^x+x)^{3/x} is e^6

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 (e^x+x)^{3/x}

x \to 0 lim ((e^{x} + x)^{\frac{3}{x}})

e^{6}

Decimal Notation

403.42879 \dots

Solution steps

x \to 0 lim ((e^{x} + x)^{\frac{3}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{3}{x} l n (e^{x} + x)})

Apply the Limit Chain Rule:

e^{6}

= e^{6}

x \to - 1 lim (2 x^{2} + x + 4)

x \to 3 lim (ln (\frac{1}{x - 3}))

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

x \to 4 lim (3 x^{2} + x - 2)

x \to 0 lim (\frac{3 sin ( 4 x )}{x})

What is the limit as x approaches 0 of (e^x+x)^{3/x} ?
The limit as x approaches 0 of (e^x+x)^{3/x} is e^6