What is the limit as x approaches 0+of (x)^{5x} ?

The limit as x approaches 0+of (x)^{5x} 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 (x)^{5x}

x \to 0 + lim ((x)^{5 x})

1

Solution steps

x \to 0 + lim (x^{5 x})

Apply exponent rules

= x \to 0 + lim (e^{5 x l n (x)})

Apply the Limit Chain Rule:

1

= 1

x \to 0 + lim (e^{\frac{6}{x}})

x \to \frac{π}{4} lim (\frac{x}{tan ( x )})

x \to - 1 lim (x^{4} - 4 x^{3} + 5)

x \to \infty + lim (1)

x \to \frac{24}{5} lim (5 x - 2)

What is the limit as x approaches 0+of (x)^{5x} ?
The limit as x approaches 0+of (x)^{5x} is 1