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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

4 \frac{d ^{2} x}{d t ^{2}} + 7 \frac{d x}{d t} + 15 x = 0

x \to 10 - lim (\frac{- 8}{x - 10})

y = arccos (x) + x

5 x^{4}

\frac{\partial}{\partial x} (4 - x^{2} + x y - 3 y^{2})

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