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

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

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

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

- \infty

Solution steps

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

Divide by highest denominator power:

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

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

For

x

approaching

- 2

from the right

, x > - 2 \Rightarrow 1 - \frac{4}{x ^{2}} < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

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

x \to 0 + lim (x^{l n (1 + x)})

x \to - 3 lim (\frac{5}{( x + 3 ) ^{3}})

x \to 0 lim (7 x ln (x))

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

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