What is the limit as x approaches infinity of ((x-3)/(x-4))^{-x} ?

The limit as x approaches infinity of ((x-3)/(x-4))^{-x} is 1/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-3)/(x-4))^{-x}

x \to \infty lim ((\frac{x - 3}{x - 4})^{- x})

\frac{1}{e}

Decimal Notation

0.36787 \dots

Solution steps

x \to \infty lim ((\frac{x - 3}{x - 4})^{- x})

Apply exponent rules

= x \to \infty lim (e^{- x l n (\frac{x - 3}{x - 4})})

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

\frac{d}{d x} (ln (sinh (5 x)))

y = (3 x - 2 x^{2})^{3}

\frac{9 + 6 x}{7 - 4 x}

y = e^{x} (p + p p)

ln (2 - 3 x)

What is the limit as x approaches infinity of ((x-3)/(x-4))^{-x} ?
The limit as x approaches infinity of ((x-3)/(x-4))^{-x} is 1/e