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

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

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

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

\infty

Solution steps

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

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

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

x \to 2 + lim (x^{2} + 2) = 6

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

= 6 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

t \to 0 lim (\frac{5 ^{t} - 1}{t})

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

x \to 4 lim ([\frac{x ^{2} + 4}{5}])

x \to 4 - lim (\frac{x + 1}{x - 4})

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

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