What is the limit as a approaches 0 of (a-1)^a ?

The limit as a approaches 0 of (a-1)^a is 1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as a approaches 0 of (a-1)^a

a \to 0 lim ((a - 1)^{a})

1

Solution steps

a \to 0 lim ((a - 1)^{a})

Plug in the value

a = 0

= (0 - 1)^{0}

Simplify

= 1

x \to - 3 lim (\frac{x ^{3} + 5 x ^{2} - 3 x - 9}{x ^{3} + 7 x ^{2} + 15 x + 9})

x \to 3 lim (\frac{3}{2 x - 6})

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

x \to 1 lim (- 3 x^{4} + 2 x + 1)

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

What is the limit as a approaches 0 of (a-1)^a ?
The limit as a approaches 0 of (a-1)^a is 1