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

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

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

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

- \infty

Solution steps

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

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

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

Divide by highest denominator power:

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

= 3 \cdot 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

= 3 (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

x \to + 0 lim (sin (\frac{1}{x}))

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

x \to 1 lim (4 x^{2} - 13 x + 12)

x \to 0 lim (2 - 4 x + 7 x^{2})

h \to 0 lim (cot (h) - csc (h))

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