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

The limit as x approaches-infinity of (x^2)/(4-x^2) is -1

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

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

- 1

Solution steps

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

Divide by highest denominator power:

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

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

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

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

x \to - \infty lim (1) = 1

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

= \frac{1}{- 1}

Simplify

= - 1

\int \frac{1}{2 + y ^{2}} d y

d er i v a t i v e cot^{6} (x)

y^{^{''}} + 25 y = t sin (2 t)

\frac{d}{d x} (0.5 e^{- 0.5 (x - 1)})

\frac{\partial}{\partial x} (\frac{1}{2 cos ^{2} ( x )})

What is the limit as x approaches-infinity of (x^2)/(4-x^2) ?
The limit as x approaches-infinity of (x^2)/(4-x^2) is -1