What is the limit as x approaches 0+of (1+3/x)^{2x} ?

The limit as x approaches 0+of (1+3/x)^{2x} is 1

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+3/x)^{2x}

x \to 0 + lim ((1 + \frac{3}{x})^{2 x})

1

Solution steps

x \to 0 + lim ((1 + \frac{3}{x})^{2 x})

Apply exponent rules

= x \to 0 + lim (e^{2 x l n (1 + \frac{3}{x})})

Apply the Limit Chain Rule:

1

= 1

x \to 2 lim (\frac{x ^{2} - 5}{x - 2})

x \to 0 + lim (x^{π x})

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

x \to 4 lim (x^{2} + 5 x - 35)

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

What is the limit as x approaches 0+of (1+3/x)^{2x} ?
The limit as x approaches 0+of (1+3/x)^{2x} is 1