What is the limit as x approaches 2-of x/(4-x^2) ?

The limit as x approaches 2-of x/(4-x^2) is infinity

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limit as x approaches 2-of x/(4-x^2)

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

\infty

Solution steps

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

\frac{x}{4 - x ^{2}} = x \frac{1}{4 - x ^{2}}

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

x \to 2 - lim (x) = 2

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

= 2 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to \infty lim (- cot (x))

x \to 9 lim (x - 3)

x \to 0 lim (\frac{4 x}{cos ( x )})

x \to 0 lim (- f (x))

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

What is the limit as x approaches 2-of x/(4-x^2) ?
The limit as x approaches 2-of x/(4-x^2) is infinity