What is the limit as x approaches 2+of-(16x)/(x-2) ?

The limit as x approaches 2+of-(16x)/(x-2) is -infinity

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limit as x approaches 2+of-(16x)/(x-2)

x \to 2 + lim (- \frac{16 x}{x - 2})

- \infty

Solution steps

x \to 2 + lim (- \frac{16 x}{x - 2})

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

= - 16 \cdot x \to 2 + lim (\frac{x}{x - 2})

Divide by highest denominator power:

\frac{1}{1 - \frac{2}{x}}

= - 16 \cdot x \to 2 + lim (\frac{1}{1 - \frac{2}{x}})

For

x

approaching

2

from the right

, x > 2 \Rightarrow 1 - \frac{2}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= - 16 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

n \to 1 lim (cos (\frac{π}{n + 1}))

x \to 0 lim (x \cdot e^{(\frac{1}{x})})

x \to 0 + lim (sin (x) ln (8 x))

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

x \to 0 lim (\frac{3 x}{cos ( x )})

What is the limit as x approaches 2+of-(16x)/(x-2) ?
The limit as x approaches 2+of-(16x)/(x-2) is -infinity