What is the limit as x approaches 0 of (1+3x)^{7/x} ?

The limit as x approaches 0 of (1+3x)^{7/x} is e^{21}

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)^{7/x}

x \to 0 lim ((1 + 3 x)^{\frac{7}{x}})

e^{21}

Decimal Notation

1318815734.48321 \dots

Solution steps

x \to 0 lim ((1 + 3 x)^{\frac{7}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{7}{x} l n (1 + 3 x)})

Apply the Limit Chain Rule:

e^{21}

= e^{21}

5 sin (6 t)

\int t e^{- 4 t} d t

\frac{d}{d x} (arctan (- x))

8 e^{x} cos (x)

k = 0 \sum \infty (- \frac{3}{4})^{k}

What is the limit as x approaches 0 of (1+3x)^{7/x} ?
The limit as x approaches 0 of (1+3x)^{7/x} is e^{21}