What is the limit as x approaches 1+of x^{8/(x-1)} ?

The limit as x approaches 1+of x^{8/(x-1)} is e^8

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limit as x approaches 1+of x^{8/(x-1)}

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

e^{8}

Decimal

2980.95798 \dots

Solution steps

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

Apply exponent rules

= x \to 1 + lim (e^{\frac{8}{x - 1} l n (x)})

Apply the Limit Chain Rule:

e^{8}

= e^{8}

x \to - 7 - lim (\frac{∣ x + 7 ∣}{x + 7})

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

x \to \infty lim (\frac{1}{2} \cdot x)

x \to - 2 lim (9 - x^{2})

x \to 1 lim (\frac{ln ( x )}{1 - 1})

What is the limit as x approaches 1+of x^{8/(x-1)} ?
The limit as x approaches 1+of x^{8/(x-1)} is e^8