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}

\frac{d ^{2}}{d x ^{2}} (\frac{( x - 3 ) ( x ^{2} + 3 x + 9 )}{x ^{3}})

\int - \frac{1}{5} cos (5 x) d x

\int \frac{( 2 x ^{2} + x + 4 )}{x ^{3} + 4 x ^{2}} d x

\frac{d}{d x} (x^{3} + 6)

y^{'} (x)

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