What is the limit as x approaches 0+of-5/x ?

The limit as x approaches 0+of-5/x is -infinity

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limit as x approaches 0+of-5/x

x \to 0 + lim (- \frac{5}{x})

- \infty

Solution steps

x \to 0 + lim (- \frac{5}{x})

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

= - 5 \cdot x \to 0 + lim (\frac{1}{x})

For

x

approaching

0

from the right

, x > 0 \Rightarrow x > 0

The denominator is a positive quantity approaching 0 from the right

= - 5 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

What is the limit as x approaches 0+of-5/x ?
The limit as x approaches 0+of-5/x is -infinity