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

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

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

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

\infty

Solution steps

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

Divide by highest denominator power:

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

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

For

x

approaching

2

from the left

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

The denominator is a positive quantity approaching 0 from the right

= \infty

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\frac{d}{d x} (3 x^{2} y)

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