What is the limit as x approaches 1-of (2x)/(x-1) ?

The limit as x approaches 1-of (2x)/(x-1) is -infinity

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limit as x approaches 1-of (2x)/(x-1)

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

- \infty

Solution steps

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

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

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

Divide by highest denominator power:

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

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

For

x

approaching

1

from the left

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

The denominator is a negative quantity approaching 0 from the left

= 2 (- \infty)

Apply Infinity Property:

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

= - \infty

x \to π lim (e^{t a n (x)})

x \to - 8 lim (\frac{3 - 4 x}{x + 8})

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

x \to 2 lim (8 + 12 x - 3 x)

x \to - \infty lim (π^{x})

What is the limit as x approaches 1-of (2x)/(x-1) ?
The limit as x approaches 1-of (2x)/(x-1) is -infinity