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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\int (x^{2} - 1)^{4} d x

\frac{d}{d x} (\frac{( x + 2 )}{( x - 1 )})

x^{12}

\int sin^{4} (5 x) cos^{6} (5 x) d x

\frac{d}{d x} (- 5 x^{- 6})

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