What is the limit as x approaches 0-of (2x+9)/(-x) ?

The limit as x approaches 0-of (2x+9)/(-x) is infinity

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limit as x approaches 0-of (2x+9)/(-x)

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

\infty

Solution steps

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

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

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

Divide by highest denominator power:

2 + \frac{9}{x}

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

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

With the exception of indeterminate form

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

x \to 0 - lim (2) = 2

x \to 0 - lim (\frac{9}{x}) = - \infty

= - (2 - \infty)

Simplify

- (2 - \infty) : \infty

= \infty

x \to 3 lim ([2 f (x) + 3 g (x)])

x \to 0 lim (x^{2} - x - ln (x))

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

x \to 7 lim (\frac{[ x ] - x}{x - 7})

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

What is the limit as x approaches 0-of (2x+9)/(-x) ?
The limit as x approaches 0-of (2x+9)/(-x) is infinity