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

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

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limit as x approaches infinity of (x/(x+1))^{2x}

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

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

Decimal Notation

0.13533 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

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

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

\frac{d}{d x} (a x^{3} + b x^{2})

\frac{d}{d x} (\frac{- 3}{x + 1})

n = 1 \sum \infty \frac{n ^{8}}{n !}

\frac{d}{d x} (x^{3} - x^{2} - 6 x)

\frac{d}{d x} ((x^{- 2} + x)^{3})

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