What is the limit as x approaches-2+of (x-1)/(x^2-4) ?

The limit as x approaches-2+of (x-1)/(x^2-4) is infinity

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limit as x approaches-2+of (x-1)/(x^2-4)

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

\infty

Solution steps

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

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

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

x \to - 2 + lim (x - 1) = - 3

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

= (- 3) (- \infty)

Apply Infinity Property:

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

= \infty

f (x) = \frac{7 x ^{2} - x + 9}{6 - 7 x}

\int x (\frac{1}{1 - x ^{2}}) d x

2 (3 x^{2} ln (10 x) + x^{2})

\int (- x^{3} - 8 x + 5) d x

\int_{0}^{2 π} 5 x^{2} sin (\frac{1}{4} x) d x

What is the limit as x approaches-2+of (x-1)/(x^2-4) ?
The limit as x approaches-2+of (x-1)/(x^2-4) is infinity