What is the limit as x approaches 0+of |x|^x ?

The limit as x approaches 0+of |x|^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 |x|^x

x \to 0 + lim (∣ x ∣^{x})

1

Solution steps

x \to 0 + lim (∣ x ∣^{x})

x

is positive when

x \to 0 +

. Therefore

∣ x ∣ = x

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

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

x \to 5 lim (\frac{- 1}{x - 5})

x \to \infty lim (\frac{20}{x})

x \to 2 lim (\frac{5 x - 2}{4 x + 1})

x \to \infty lim (x 2^{x})

What is the limit as x approaches 0+of |x|^x ?
The limit as x approaches 0+of |x|^x is 1