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})

Multiply by the conjugate of

x - 1 : \frac{x ^{2} - 1}{x + 1}

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

Simplify

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

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

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

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

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

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

= 1 \cdot (- \infty)

Apply Infinity Property:

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

= - \infty

x \to 0 lim (x [x] cot (x))

b \to \infty lim (e^{- b})

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

x \to - \infty lim (7^{x})

x \to π lim (\frac{cos ( 2 x )}{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