What is the limit as x approaches 2+of (x^2-2x-8)/(x^2-5x+6) ?

The limit as x approaches 2+of (x^2-2x-8)/(x^2-5x+6) is infinity

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limit as x approaches 2+of (x^2-2x-8)/(x^2-5x+6)

x \to 2 + lim (\frac{x ^{2} - 2 x - 8}{x ^{2} - 5 x + 6})

\infty

Solution steps

x \to 2 + lim (\frac{x ^{2} - 2 x - 8}{x ^{2} - 5 x + 6})

\frac{x ^{2} - 2 x - 8}{x ^{2} - 5 x + 6} = (x^{2} - 2 x - 8) \frac{1}{x ^{2} - 5 x + 6}

= x \to 2 + lim ((x^{2} - 2 x - 8) \frac{1}{x ^{2} - 5 x + 6})

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} - 2 x - 8) \cdot x \to 2 + lim (\frac{1}{x ^{2} - 5 x + 6})

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

x \to 2 + lim (\frac{1}{x ^{2} - 5 x + 6}) = - \infty

= (- 8) (- \infty)

Apply Infinity Property:

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

= \infty

\int \frac{x + 4}{x ^{2} + 8 x + 17} d x

\frac{d}{d x} (2 + \frac{1}{x})

f (x) = x (x + 1)^{2}

\frac{\partial}{\partial x} (2 x^{2} + 3 y^{2} - z^{2})

y = 4 + x x, (1, 5)

What is the limit as x approaches 2+of (x^2-2x-8)/(x^2-5x+6) ?
The limit as x approaches 2+of (x^2-2x-8)/(x^2-5x+6) is infinity