What is the limit as x approaches 1+of x^{3/(x-1)} ?

The limit as x approaches 1+of x^{3/(x-1)} is e^3

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limit as x approaches 1+of x^{3/(x-1)}

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

e^{3}

Decimal

20.08553 \dots

Solution steps

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

Apply exponent rules

= x \to 1 + lim (e^{\frac{3}{x - 1} l n (x)})

Apply the Limit Chain Rule:

e^{3}

= e^{3}

x \to \frac{π}{2} lim (cot^{2} (x))

x \to \infty lim (\frac{4}{9})

x \to - \infty lim (8)

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

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

What is the limit as x approaches 1+of x^{3/(x-1)} ?
The limit as x approaches 1+of x^{3/(x-1)} is e^3