What is the limit as x approaches infinity of ((x+1)/(x+3))^{x/5} ?

The limit as x approaches infinity of ((x+1)/(x+3))^{x/5} is 1/(e^{2/5)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches infinity of ((x+1)/(x+3))^{x/5}

x \to \infty lim ((\frac{x + 1}{x + 3})^{\frac{x}{5}})

\frac{1}{e ^{\frac{2}{5}}}

Decimal

0.67032 \dots

Solution steps

x \to \infty lim ((\frac{x + 1}{x + 3})^{\frac{x}{5}})

Apply exponent rules

= x \to \infty lim (e^{\frac{x}{5} l n (\frac{x + 1}{x + 3})})

Apply the Limit Chain Rule:

\frac{1}{e ^{\frac{2}{5}}}

= \frac{1}{e ^{\frac{2}{5}}}

What is the limit as x approaches infinity of ((x+1)/(x+3))^{x/5} ?
The limit as x approaches infinity of ((x+1)/(x+3))^{x/5} is 1/(e^{2/5)}