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

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

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

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

- \infty

Solution steps

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

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

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

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

x \to 4 - lim (2 x + 2) = 10

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

= 10 (- \infty)

Apply Infinity Property:

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

= - \infty

x \to 2 - lim (\frac{x - 3}{x ^{2} - 4})

x \to - 5 lim (x - 8)

x \to - 2 lim (x^{3} - 2 x^{2} + 4 x - 8)

x \to \infty lim (\frac{3 e ^{x} - 4}{5 e ^{x} + 2})

x \to 0 + lim (x arctan (\frac{1}{x}))

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