What is the limit as x approaches 3-of x/(x-3) ?

The limit as x approaches 3-of x/(x-3) is -infinity

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limit as x approaches 3-of x/(x-3)

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

- \infty

Solution steps

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

Divide by highest denominator power:

\frac{1}{1 - \frac{3}{x}}

= x \to 3 - lim (\frac{1}{1 - \frac{3}{x}})

For

x

approaching

3

from the left

, x < 3 \Rightarrow 1 - \frac{3}{x} < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

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What is the limit as x approaches 3-of x/(x-3) ?
The limit as x approaches 3-of x/(x-3) is -infinity