What is the limit as x approaches-2-of (3x-6)/(x+2) ?

The limit as x approaches-2-of (3x-6)/(x+2) is infinity

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limit as x approaches-2-of (3x-6)/(x+2)

x \to - 2 - lim (\frac{3 x - 6}{x + 2})

\infty

Solution steps

x \to - 2 - lim (\frac{3 x - 6}{x + 2})

Factor out

3 x

from

3 x - 6 : 3 x (1 - \frac{6}{3 x})

= x \to - 2 - lim (\frac{3 x ( 1 - \frac{6}{3 x} )}{x + 2})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3 \cdot x \to - 2 - lim (\frac{x ( 1 - \frac{6}{3 x} )}{x + 2})

Simplify

\frac{x ( 1 - \frac{6}{3 x} )}{x + 2} : \frac{x - 2}{x + 2}

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

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

= 3 \cdot x \to - 2 - lim ((x - 2) \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

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

x \to - 2 - lim (x - 2) = - 4

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

= 3 (- 4) (- \infty)

Apply Infinity Property:

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

= \infty

\frac{d}{d x} (\frac{π}{4} x)

\int \frac{sec ( θ ) tan ( θ )}{1 + sec ( θ )} d θ

f (x) = - 5 x^{2}, at x = 2

x \to 8 lim (x^{3} + 1)

\int_{3}^{5} \frac{y ^{2}}{5} + \frac{5}{4 y ^{2}} d y

What is the limit as x approaches-2-of (3x-6)/(x+2) ?
The limit as x approaches-2-of (3x-6)/(x+2) is infinity