What is the limit as x approaches 2+of (x-3)/(x^2-4) ?

The limit as x approaches 2+of (x-3)/(x^2-4) is -infinity

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limit as x approaches 2+of (x-3)/(x^2-4)

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

- \infty

Solution steps

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

\frac{x - 3}{x ^{2} - 4} = (x - 3) \frac{1}{x ^{2} - 4}

= x \to 2 + lim ((x - 3) \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 - 3) \cdot x \to 2 + lim (\frac{1}{x ^{2} - 4})

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

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

= (- 1) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

\frac{\partial}{\partial y} (x^{4} + 8 x y^{7})

\int \frac{ln ∣ x ∣}{x} d x

f (t) = (3 t - 1)^{4} (2 t + 1)^{- 3}

x \to 0 lim (\frac{tan ( k x )}{x})

\int z^{3} e^{z} d z

What is the limit as x approaches 2+of (x-3)/(x^2-4) ?
The limit as x approaches 2+of (x-3)/(x^2-4) is -infinity