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})

\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 (- \infty)

Apply Infinity Property:

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

= - \infty

\int (8 x - 2 x) d x

\frac{d}{d x} (arctan (\frac{1}{x ^{2}}))

\frac{\partial}{\partial x} (8 x^{2} - 16 y^{3})

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

\int (- 4 + tan^{2} (x)) d x

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