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

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

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

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

- \infty

Solution steps

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

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

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

x \to - 2 - lim (x^{2} - x) = 6

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

= 6 (- \infty)

Apply Infinity Property:

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

= - \infty

x \to 4 lim (\frac{x ^{3} - 8 x ^{2} + 18 x - 8}{x - 4})

x \to 0 - lim (\frac{1}{cos ( x )})

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

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

x \to 3 + lim (\frac{7 x - 5}{x - 3})

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