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 left

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

The denominator is a positive quantity approaching 0 from the right

= \infty

\int \frac{1}{- x ^{2} + 2 x} d x

\int_{0}^{0.4} e^{- x^{2}} d x

(3 + x^{2}) d y + 2 \cdot x \cdot y \cdot d x = cos (x) d x

\int \frac{1}{( 6 - 5 x ) ^{2}} d x

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