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-1/(3*x^3)
Limit of the function/ -1/(3*x^3)

Limit of the function -1/(3*x^3)

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The solution

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     /-1  \
 lim |----|
x->0+|   3|
     \3*x /
lim⁡x→0+(−13x3)\lim_{x \to 0^+}\left(- \frac{1}{3 x^{3}}\right) 
Limit(-1/(3*x^3), x, 0)
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
02468-8-6-4-2-1010-20000001000000
Plot the graph
Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(−13x3)=−∞\lim_{x \to 0^-}\left(- \frac{1}{3 x^{3}}\right) = -\infty
More at x→0 from the left
lim⁡x→0+(−13x3)=−∞\lim_{x \to 0^+}\left(- \frac{1}{3 x^{3}}\right) = -\infty
lim⁡x→∞(−13x3)=0\lim_{x \to \infty}\left(- \frac{1}{3 x^{3}}\right) = 0
More at x→oo
lim⁡x→1−(−13x3)=−13\lim_{x \to 1^-}\left(- \frac{1}{3 x^{3}}\right) = - \frac{1}{3}
More at x→1 from the left
lim⁡x→1+(−13x3)=−13\lim_{x \to 1^+}\left(- \frac{1}{3 x^{3}}\right) = - \frac{1}{3}
More at x→1 from the right
lim⁡x→−∞(−13x3)=0\lim_{x \to -\infty}\left(- \frac{1}{3 x^{3}}\right) = 0
More at x→-oo
One‐sided limits [src] 
     /-1  \
 lim |----|
x->0+|   3|
     \3*x /
lim⁡x→0+(−13x3)\lim_{x \to 0^+}\left(- \frac{1}{3 x^{3}}\right) 
-oo
−∞-\infty 
= -1147650.33333333
     /-1  \
 lim |----|
x->0-|   3|
     \3*x /
lim⁡x→0−(−13x3)\lim_{x \to 0^-}\left(- \frac{1}{3 x^{3}}\right) 
oo
∞\infty 
= 1147650.33333333
= 1147650.33333333
Numerical answer [src] 
-1147650.33333333
-1147650.33333333
The graph
Limit of the function -1/(3*x^3)
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