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

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

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

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

\infty

Solution steps

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

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

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

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

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

= 3 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 0 lim ((4 x - 1)^{2 x + 1})

x \to 0 lim (\frac{x ^{3}}{2 x ^{2}})

x \to 2 + lim (5 - x)

x \to - 8 lim (5)

x \to - 4 lim (\frac{x + 4}{4 x + 16})

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