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

The limit as x approaches infinity of (((x+1))/(x-1))^{x-1} is e^2

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))/(x-1))^{x-1}

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

e^{2}

Decimal

7.38905 \dots

Solution steps

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

Simplify

(\frac{x + 1}{x - 1})^{x - 1} : (\frac{x + 1}{x - 1})^{x} (\frac{x + 1}{x - 1})^{- 1}

= x \to \infty lim ((\frac{x + 1}{x - 1})^{x} (\frac{x + 1}{x - 1})^{- 1})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to \infty lim ((\frac{x + 1}{x - 1})^{x}) \cdot x \to \infty lim ((\frac{x + 1}{x - 1})^{- 1})

x \to \infty lim ((\frac{x + 1}{x - 1})^{x}) = e^{2}

x \to \infty lim ((\frac{x + 1}{x - 1})^{- 1}) = 1

= e^{2} \cdot 1

Simplify

= e^{2}

x \to 2 + lim (\frac{x + 1}{x ^{2} - 5 x + 6})

x \to π lim (x - 3.1416)

x \to \infty lim (1 + \frac{3}{4})

x \to 0 + lim (csc (x) cot (x))

x \to - 4 + lim (\frac{x + 4}{∣ x + 4 ∣})

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