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 \infty lim (\frac{( x ^{13} )}{e ^{x}})

x \to - 2 lim (3 x - \frac{6}{x})

y \to 0 lim (\frac{cos ( y )}{y})

x \to 0 lim ((9^{x} + x)^{\frac{2}{x}})

x \to 3 lim (3 x^{2} + x)

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