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

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

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

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

\infty

Solution steps

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

Apply the following algebraic property

: a + b = a (1 + \frac{b}{a})

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

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

Cancel the common factor:

x

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

For

x

approaching

- 2

from the right

, x > - 2 \Rightarrow x (- \frac{4}{x ^{2}} + 1) > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

3 x^{2} + 4 x + 1

\frac{d}{d x} (\frac{x}{2 x - 1})

\frac{d y}{d t} = - 4 y

\int 100 x d x

4 π r^{2}

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