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

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

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

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

- \infty

Solution steps

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

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

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

x \to 2 - lim (x^{2} + 4) = 8

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

= 8 (- \infty)

Apply Infinity Property:

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

= - \infty

\int 4 x e^{x} d x

t \to 0 + lim (t + 1)

\int \frac{x ^{2}}{cos ^{2} ( x )} d x

\int 3 v (v^{2} + 6)^{2} d v

\frac{\partial}{\partial x} (4 x^{3} y^{3} - 4)

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