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

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

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

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

e^{2}

Decimal Notation

7.38905 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{2}

= e^{2}

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

x \to - 4 lim (\frac{1}{( x + 4 ) ^{2}})

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

x \to \frac{π}{2} lim ((2 x - π) tan (x))

x \to 1 + lim (tan (x - 1))

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