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 negative quantity approaching 0 from the left

= - \infty

\frac{\partial}{\partial y} (x e^{y} - y e^{x})

\frac{\partial}{\partial x} (e^{x} - x^{2} arctan (x))

\frac{6 ( t + 1 ) d y}{d t} - 5 y = 5 t, y (0) = 4

g (x) = - x

\frac{d y}{d x} = 2 y - x y^{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