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

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

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limit as x approaches 2+of (|x|+2)/(x-2)

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

\infty

Solution steps

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

x

is positive when

x \to 2 +

. Therefore

∣ x ∣ = x

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

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

= 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

= 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

= 4 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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