What is the limit as x approaches 2+of (x+1)/(3x-6) ?

The limit as x approaches 2+of (x+1)/(3x-6) is infinity

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limit as x approaches 2+of (x+1)/(3x-6)

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

\infty

Solution steps

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

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

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

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

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

= 3 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

What is the limit as x approaches 2+of (x+1)/(3x-6) ?
The limit as x approaches 2+of (x+1)/(3x-6) is infinity