What is the limit as x approaches 4-of (3x)/(x-4) ?

The limit as x approaches 4-of (3x)/(x-4) is -infinity

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limit as x approaches 4-of (3x)/(x-4)

x \to 4 - lim (\frac{3 x}{x - 4})

- \infty

Solution steps

x \to 4 - lim (\frac{3 x}{x - 4})

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

= 3 \cdot x \to 4 - lim (\frac{x}{x - 4})

Divide by highest denominator power:

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

= 3 \cdot x \to 4 - lim (\frac{1}{1 - \frac{4}{x}})

For

x

approaching

4

from the left

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

The denominator is a negative quantity approaching 0 from the left

= 3 (- \infty)

Apply Infinity Property:

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

= - \infty

\int 2 x (x^{2} + 7)^{5} d x

(0, 5), (3, - 5)

\int \frac{1}{x ( 1 - x ) ^{2}} d x

\int_{1}^{5} 10

(0, 0), (5, - 1)

What is the limit as x approaches 4-of (3x)/(x-4) ?
The limit as x approaches 4-of (3x)/(x-4) is -infinity