What is the limit as x approaches infinity of \sqrt[x]{x/(x+1)} ?

The limit as x approaches infinity of \sqrt[x]{x/(x+1)} is 1

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limit as x approaches infinity of \sqrt[x]{x/(x+1)}

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

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

x \to 0 lim (\frac{- x - ln ( 1 - x )}{8 x ^{2}})

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

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

x \to 0 lim (\frac{csc ^{2} ( x )}{cot ^{2} ( x )})

What is the limit as x approaches infinity of \sqrt[x]{x/(x+1)} ?
The limit as x approaches infinity of \sqrt[x]{x/(x+1)} is 1