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12*x^2
Limit of the function/ 12*x^2

Limit of the function 12*x^2

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The solution

You have entered [src] 
     /    2\
 lim \12*x /
x->oo
lim⁡x→∞(12x2)\lim_{x \to \infty}\left(12 x^{2}\right) 
Limit(12*x^2, x, oo, dir='-')
Detail solution
Let's take the limit
lim⁡x→∞(12x2)\lim_{x \to \infty}\left(12 x^{2}\right)
Let's divide numerator and denominator by x^2:
lim⁡x→∞(12x2)\lim_{x \to \infty}\left(12 x^{2}\right) =
lim⁡x→∞11121x2\lim_{x \to \infty} \frac{1}{\frac{1}{12} \frac{1}{x^{2}}}
Do Replacement
u=1xu = \frac{1}{x}
then
lim⁡x→∞11121x2=lim⁡u→0+(12u2)\lim_{x \to \infty} \frac{1}{\frac{1}{12} \frac{1}{x^{2}}} = \lim_{u \to 0^+}\left(\frac{12}{u^{2}}\right)
=
120=∞\frac{12}{0} = \infty

The final answer:
lim⁡x→∞(12x2)=∞\lim_{x \to \infty}\left(12 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
02468-8-6-4-2-101002000
Plot the graph
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(12x2)=∞\lim_{x \to \infty}\left(12 x^{2}\right) = \infty
lim⁡x→0−(12x2)=0\lim_{x \to 0^-}\left(12 x^{2}\right) = 0
More at x→0 from the left
lim⁡x→0+(12x2)=0\lim_{x \to 0^+}\left(12 x^{2}\right) = 0
More at x→0 from the right
lim⁡x→1−(12x2)=12\lim_{x \to 1^-}\left(12 x^{2}\right) = 12
More at x→1 from the left
lim⁡x→1+(12x2)=12\lim_{x \to 1^+}\left(12 x^{2}\right) = 12
More at x→1 from the right
lim⁡x→−∞(12x2)=∞\lim_{x \to -\infty}\left(12 x^{2}\right) = \infty
More at x→-oo
The graph
Limit of the function 12*x^2
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