What is the limit as x approaches 9-of (x^9)/(x-9) ?

The limit as x approaches 9-of (x^9)/(x-9) is -infinity

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limit as x approaches 9-of (x^9)/(x-9)

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

- \infty

Solution steps

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

\frac{x ^{9}}{x - 9} = x^{9} \frac{1}{x - 9}

= x \to 9 - lim (x^{9} \frac{1}{x - 9})

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 9 - lim (x^{9}) \cdot x \to 9 - lim (\frac{1}{x - 9})

x \to 9 - lim (x^{9}) = 387420489

x \to 9 - lim (\frac{1}{x - 9}) = - \infty

= 387420489 (- \infty)

Apply Infinity Property:

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

= - \infty

x \to 0 + lim (x ln (x^{6}))

\frac{6 x}{( x + 1 )}

\int \frac{7 x ^{2} + x + 54}{x ^{3} + 9 x} d x

y = x + 2

\frac{d}{d x} (\frac{5}{25 x ^{2} + 1})

What is the limit as x approaches 9-of (x^9)/(x-9) ?
The limit as x approaches 9-of (x^9)/(x-9) is -infinity