What is the limit as x approaches 0+of (x/(x+1))^x ?

The limit as x approaches 0+of (x/(x+1))^x is 1

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limit as x approaches 0+of (x/(x+1))^x

x \to 0 + lim ((\frac{x}{x + 1})^{x})

1

Solution steps

x \to 0 + lim ((\frac{x}{x + 1})^{x})

Apply exponent rules

= x \to 0 + lim (e^{x l n (\frac{x}{x + 1})})

Apply the Limit Chain Rule:

1

= 1

x \to 0 lim (\frac{9 x ^{4}}{5 x ^{4}} - 12)

n \to \infty lim (\frac{ln ( \frac{1}{n} )}{2 n})

x \to π + lim (cos (x))

u \to - 2 lim (\frac{u ^{3} + 4 u ^{2} + 4 u}{( u + 2 ) ( u - 3 )})

x \to 0 + lim (\frac{1}{x} + 5 x^{3} + 3)

What is the limit as x approaches 0+of (x/(x+1))^x ?
The limit as x approaches 0+of (x/(x+1))^x is 1