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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

x \to - \infty lim (e^{x} + 3)

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

x \to 3 - lim (\frac{5 x}{x - 3})

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

x \to a lim (3 x^{2} + 4 x - 5)

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