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

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

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

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

- \infty

Solution steps

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

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

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

Divide by highest denominator power:

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

= 4 \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

= 4 (- \infty)

Apply Infinity Property:

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

= - \infty

\frac{d}{d x} (\frac{x}{y} + \frac{y}{x})

\int_{2}^{4} (x^{2} + 2)^{3} d x

y^{^{''}} + y = t, y (0) = 1, y (1) = - 2

h \to 0 lim (\frac{( 3 + h ) ^{4} - 81}{h})

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{8 x ^{\frac{7}{8}}})

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