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

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

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

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

- \infty

Solution steps

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

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

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

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

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

= 4 (- \infty)

Apply Infinity Property:

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

= - \infty

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

x \to 0 lim (x^{3} + 2 x)

x \to 0 lim (\frac{tan ( 5 x )}{7 x})

x \to - 8 lim (5)

x \to 0 + lim (x^{x - 1})

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