What is the limit as x approaches 0 of (1+3x)^{1/x} ?

The limit as x approaches 0 of (1+3x)^{1/x} is e^3

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+3x)^{1/x}

x \to 0 lim ((1 + 3 x)^{\frac{1}{x}})

e^{3}

Decimal Notation

20.08553 \dots

Solution steps

x \to 0 lim ((1 + 3 x)^{\frac{1}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x} l n (1 + 3 x)})

Apply the Limit Chain Rule:

e^{3}

= e^{3}

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} + 3 z^{2} - 9)

\int_{2}^{6} ln (x) d x

x \to - 3 lim (\frac{x ^{2} - 9}{x + 3})

f (x) = sin (sin (x)), at x = (4 π)

\int cos (2 x) + 1 d x

What is the limit as x approaches 0 of (1+3x)^{1/x} ?
The limit as x approaches 0 of (1+3x)^{1/x} is e^3