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-5*x^2
Limit of the function/ -5*x^2

Limit of the function -5*x^2

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     /    2\
 lim \-5*x /
x->oo
lim⁡x→∞(−5x2)\lim_{x \to \infty}\left(- 5 x^{2}\right) 
Limit(-5*x^2, x, oo, dir='-')
Detail solution
Let's take the limit
lim⁡x→∞(−5x2)\lim_{x \to \infty}\left(- 5 x^{2}\right)
Let's divide numerator and denominator by x^2:
lim⁡x→∞(−5x2)\lim_{x \to \infty}\left(- 5 x^{2}\right) =
lim⁡x→∞1(−1)151x2\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{5} \frac{1}{x^{2}}}
Do Replacement
u=1xu = \frac{1}{x}
then
lim⁡x→∞1(−1)151x2=lim⁡u→0+(−5u2)\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{5} \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(- \frac{5}{u^{2}}\right)
=
−50=−∞- \frac{5}{0} = -\infty

The final answer:
lim⁡x→∞(−5x2)=−∞\lim_{x \to \infty}\left(- 5 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
02468-8-6-4-2-1010-1000500
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Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(−5x2)=−∞\lim_{x \to \infty}\left(- 5 x^{2}\right) = -\infty
lim⁡x→0−(−5x2)=0\lim_{x \to 0^-}\left(- 5 x^{2}\right) = 0
More at x→0 from the left
lim⁡x→0+(−5x2)=0\lim_{x \to 0^+}\left(- 5 x^{2}\right) = 0
More at x→0 from the right
lim⁡x→1−(−5x2)=−5\lim_{x \to 1^-}\left(- 5 x^{2}\right) = -5
More at x→1 from the left
lim⁡x→1+(−5x2)=−5\lim_{x \to 1^+}\left(- 5 x^{2}\right) = -5
More at x→1 from the right
lim⁡x→−∞(−5x2)=−∞\lim_{x \to -\infty}\left(- 5 x^{2}\right) = -\infty
More at x→-oo
The graph
Limit of the function -5*x^2
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