What is the limit as x approaches infinity of (x-1)^{1/(ln(x))} ?

The limit as x approaches infinity of (x-1)^{1/(ln(x))} is e

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches infinity of (x-1)^{1/(ln(x))}

x \to \infty lim ((x - 1)^{\frac{1}{l n ( x )}})

e

Decimal

2.71828 \dots

Solution steps

x \to \infty lim ((x - 1)^{\frac{1}{l n ( x )}})

Apply exponent rules

= x \to \infty lim (e^{\frac{1}{l n ( x )} l n (x - 1)})

Apply the Limit Chain Rule:

e

= e

\frac{d}{d x} (e^{p (t, x) t} \cdot cos (n t))

\frac{\partial}{\partial x} (6 - x^{2} + 2 y^{2})

\frac{d}{d x} (A x^{2})

\int \frac{x + 3}{x ^{2} - 2 x - 3} d x

\int f (x + b) d x

What is the limit as x approaches infinity of (x-1)^{1/(ln(x))} ?
The limit as x approaches infinity of (x-1)^{1/(ln(x))} is e