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

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

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

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

- \infty

Solution steps

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

Rationalize numerator

\frac{- x}{x} : - \frac{1}{- x}

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

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

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

For

x

approaching

0

from the left

, x < 0 \Rightarrow - x > 0

The denominator is a positive quantity approaching 0 from the right

= - \infty

x \to 1 lim (2 x^{2} + x - 3)

x \to 0 + lim (\frac{( cos ( x ) )}{x})

x \to 0 lim (x^{2} + x - 7)

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

x \to \infty lim (x^{(\frac{l n ( 3 )}{1 + l n ( x )})})

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