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 right

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

The denominator is a negative quantity approaching 0 from the left

= - \infty

\int \frac{e ^{x}}{1 + 16 e ^{2 x}} d x

3 x + 1

(y^{2} + y x) d x - (x^{2}) d y = 0

x \to 2 lim (x^{2} + 8)

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