What is the limit as x approaches 1+of x^{4/(x-1)} ?

The limit as x approaches 1+of x^{4/(x-1)} is e^4

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limit as x approaches 1+of x^{4/(x-1)}

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

e^{4}

Decimal Notation

54.59815 \dots

Solution steps

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

Apply exponent rules

= x \to 1 + lim (e^{\frac{4}{x - 1} l n (x)})

Apply the Limit Chain Rule:

e^{4}

= e^{4}

x \to 0 + lim (x ln (tan (x)))

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

x \to - 6 lim (\frac{∣ x ∣}{x})

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

x \to 0 lim ((\frac{1 + 5 x}{1 + 2 x})^{\frac{1}{x}})

What is the limit as x approaches 1+of x^{4/(x-1)} ?
The limit as x approaches 1+of x^{4/(x-1)} is e^4