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

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

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

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

\infty

Solution steps

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

Factor out

x

from

- 2 - x : x (- \frac{- 2}{- x} - 1)

= x \to 0 - lim (\frac{x ( - \frac{- 2}{- x} - 1 )}{x})

Simplify

\frac{x ( - \frac{- 2}{- x} - 1 )}{x} : - \frac{2}{x} - 1

= x \to 0 - lim (- \frac{2}{x} - 1)

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

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

x \to 0 - lim (1) = 1

= - (- \infty) - 1

Simplify

- (- \infty) - 1 : \infty

= \infty

x \to - 3 - lim (\frac{x ^{2} - 9}{x + 3})

x \to \infty lim (\frac{- 1}{0})

x \to 2 lim (2 x^{2} - 5 x + 6)

h \to 0 lim (\frac{6}{h})

x \to 5 lim (\frac{3 x}{∣ x - 5 ∣})

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