What is the limit as x approaches 0 of (1+8x)^{1/x} ?

The limit as x approaches 0 of (1+8x)^{1/x} is e^8

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+8x)^{1/x}

x \to 0 lim ((1 + 8 x)^{\frac{1}{x}})

e^{8}

Decimal Notation

2980.95798 \dots

Solution steps

x \to 0 lim ((1 + 8 x)^{\frac{1}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x} l n (1 + 8 x)})

Apply the Limit Chain Rule:

e^{8}

= e^{8}

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

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

θ \to π lim (θ sec (θ))

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

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

What is the limit as x approaches 0 of (1+8x)^{1/x} ?
The limit as x approaches 0 of (1+8x)^{1/x} is e^8