What is the limit as x approaches 4-of (2x)/(4-x) ?

The limit as x approaches 4-of (2x)/(4-x) is infinity

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limit as x approaches 4-of (2x)/(4-x)

x \to 4 - lim (\frac{2 x}{4 - x})

\infty

Solution steps

x \to 4 - lim (\frac{2 x}{4 - x})

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

= 2 \cdot x \to 4 - lim (\frac{x}{4 - x})

Divide by highest denominator power:

\frac{1}{\frac{4}{x} - 1}

= 2 \cdot x \to 4 - lim (\frac{1}{\frac{4}{x} - 1})

For

x

approaching

4

from the left

, x < 4 \Rightarrow \frac{4}{x} - 1 > 0

The denominator is a positive quantity approaching 0 from the right

= 2 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

What is the limit as x approaches 4-of (2x)/(4-x) ?
The limit as x approaches 4-of (2x)/(4-x) is infinity