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4*x^3
Limit of the function/ 4*x^3

Limit of the function 4*x^3

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      /   3\
 lim  \4*x /
x->-oo
lim⁡x→−∞(4x3)\lim_{x \to -\infty}\left(4 x^{3}\right) 
Limit(4*x^3, x, -oo)
Detail solution
Let's take the limit
lim⁡x→−∞(4x3)\lim_{x \to -\infty}\left(4 x^{3}\right)
Let's divide numerator and denominator by x^3:
lim⁡x→−∞(4x3)\lim_{x \to -\infty}\left(4 x^{3}\right) =
lim⁡x→−∞1141x3\lim_{x \to -\infty} \frac{1}{\frac{1}{4} \frac{1}{x^{3}}}
Do Replacement
u=1xu = \frac{1}{x}
then
lim⁡x→−∞1141x3=lim⁡u→0+(4u3)\lim_{x \to -\infty} \frac{1}{\frac{1}{4} \frac{1}{x^{3}}} = \lim_{u \to 0^+}\left(\frac{4}{u^{3}}\right)
=
40=−∞\frac{4}{0} = -\infty

The final answer:
lim⁡x→−∞(4x3)=−∞\lim_{x \to -\infty}\left(4 x^{3}\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
02468-8-6-4-2-1010-1000010000
Plot the graph
Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→−∞(4x3)=−∞\lim_{x \to -\infty}\left(4 x^{3}\right) = -\infty
lim⁡x→∞(4x3)=∞\lim_{x \to \infty}\left(4 x^{3}\right) = \infty
More at x→oo
lim⁡x→0−(4x3)=0\lim_{x \to 0^-}\left(4 x^{3}\right) = 0
More at x→0 from the left
lim⁡x→0+(4x3)=0\lim_{x \to 0^+}\left(4 x^{3}\right) = 0
More at x→0 from the right
lim⁡x→1−(4x3)=4\lim_{x \to 1^-}\left(4 x^{3}\right) = 4
More at x→1 from the left
lim⁡x→1+(4x3)=4\lim_{x \to 1^+}\left(4 x^{3}\right) = 4
More at x→1 from the right
The graph
Limit of the function 4*x^3
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