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x^3-x
Limit of the function/ x^3-x

Limit of the function x^3-x

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The solution

You have entered [src] 
     / 3    \
 lim \x  - x/
x->1+
lim⁡x→1+(x3−x)\lim_{x \to 1^+}\left(x^{3} - x\right) 
Limit(x^3 - x, x, 1)
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
-2.0-1.5-1.0-0.52.00.00.51.01.5-1010
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→1−(x3−x)=0\lim_{x \to 1^-}\left(x^{3} - x\right) = 0
More at x→1 from the left
lim⁡x→1+(x3−x)=0\lim_{x \to 1^+}\left(x^{3} - x\right) = 0
lim⁡x→∞(x3−x)=∞\lim_{x \to \infty}\left(x^{3} - x\right) = \infty
More at x→oo
lim⁡x→0−(x3−x)=0\lim_{x \to 0^-}\left(x^{3} - x\right) = 0
More at x→0 from the left
lim⁡x→0+(x3−x)=0\lim_{x \to 0^+}\left(x^{3} - x\right) = 0
More at x→0 from the right
lim⁡x→−∞(x3−x)=−∞\lim_{x \to -\infty}\left(x^{3} - x\right) = -\infty
More at x→-oo
One‐sided limits [src] 
     / 3    \
 lim \x  - x/
x->1+
lim⁡x→1+(x3−x)\lim_{x \to 1^+}\left(x^{3} - x\right) 
0
00 
= 2.48938774912321e-31
     / 3    \
 lim \x  - x/
x->1-
lim⁡x→1−(x3−x)\lim_{x \to 1^-}\left(x^{3} - x\right) 
0
00 
= -8.29922254882846e-31
= -8.29922254882846e-31
Rapid solution [src] 
0
00
Expand and simplify
Numerical answer [src] 
2.48938774912321e-31
2.48938774912321e-31
The graph
Limit of the function x^3-x
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