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

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

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

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

- \infty

Solution steps

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

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

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

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

With the exception of indeterminate form

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

x \to 2 + lim (2 - 4 x) = - 6

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

= (- 6) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

x \to 1 + lim (\frac{∣ 1 - x ∣}{x - 1})

x \to 5 lim (17 - x)

x \to 5 lim (\frac{x}{10 - 2 x})

x \to \frac{2}{3} + lim (3 x - 2)

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

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