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Limit of the function/ -x^2

Limit of the function -x^2

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     /  2\
 lim \-x /
x->oo
lim⁡x→∞(−x2)\lim_{x \to \infty}\left(- x^{2}\right) 
Limit(-x^2, x, oo, dir='-')
Detail solution
Let's take the limit
lim⁡x→∞(−x2)\lim_{x \to \infty}\left(- x^{2}\right)
Let's divide numerator and denominator by x^2:
lim⁡x→∞(−x2)\lim_{x \to \infty}\left(- x^{2}\right) =
lim⁡x→∞1(−1)1x2\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{x^{2}}}
Do Replacement
u=1xu = \frac{1}{x}
then
lim⁡x→∞1(−1)1x2=lim⁡u→0+(−1u2)\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(- \frac{1}{u^{2}}\right)
=
−10=−∞- \frac{1}{0} = -\infty

The final answer:
lim⁡x→∞(−x2)=−∞\lim_{x \to \infty}\left(- x^{2}\right) = -\infty
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
02468-8-6-4-2-1010-200100
Plot the graph
Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(−x2)=−∞\lim_{x \to \infty}\left(- x^{2}\right) = -\infty
lim⁡x→0−(−x2)=0\lim_{x \to 0^-}\left(- x^{2}\right) = 0
More at x→0 from the left
lim⁡x→0+(−x2)=0\lim_{x \to 0^+}\left(- x^{2}\right) = 0
More at x→0 from the right
lim⁡x→1−(−x2)=−1\lim_{x \to 1^-}\left(- x^{2}\right) = -1
More at x→1 from the left
lim⁡x→1+(−x2)=−1\lim_{x \to 1^+}\left(- x^{2}\right) = -1
More at x→1 from the right
lim⁡x→−∞(−x2)=−∞\lim_{x \to -\infty}\left(- x^{2}\right) = -\infty
More at x→-oo
The graph
Limit of the function -x^2
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