What is the limit as x approaches 1 of (x/(x+1))^x ?

The limit as x approaches 1 of (x/(x+1))^x is 1/2

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limit as x approaches 1 of (x/(x+1))^x

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

\frac{1}{2}

Decimal

0.5

Solution steps

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

Plug in the value

x = 1

= (\frac{1}{1 + 1})^{1}

Simplify

= \frac{1}{2}

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