What is the limit as x approaches 1+of x^{5/(x-1)} ?

The limit as x approaches 1+of x^{5/(x-1)} is e^5

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limit as x approaches 1+of x^{5/(x-1)}

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

e^{5}

Decimal

148.41315 \dots

Solution steps

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

Apply exponent rules

= x \to 1 + lim (e^{\frac{5}{x - 1} l n (x)})

Apply the Limit Chain Rule:

e^{5}

= e^{5}

x \to 0 + lim ((1 + 8 x)^{\frac{1}{x}})

x \to 7 lim (\frac{4 x}{x - 7})

x \to - 2 + lim (tan (\frac{π x}{4}))

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

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

What is the limit as x approaches 1+of x^{5/(x-1)} ?
The limit as x approaches 1+of x^{5/(x-1)} is e^5