What is the limit as x approaches 8-of (x^8)/(x-8) ?

The limit as x approaches 8-of (x^8)/(x-8) is -infinity

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limit as x approaches 8-of (x^8)/(x-8)

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

- \infty

Solution steps

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

\frac{x ^{8}}{x - 8} = x^{8} \frac{1}{x - 8}

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

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

x \to 8 - lim (x^{8}) = 16777216

x \to 8 - lim (\frac{1}{x - 8}) = - \infty

= 16777216 (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

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What is the limit as x approaches 8-of (x^8)/(x-8) ?
The limit as x approaches 8-of (x^8)/(x-8) is -infinity