Mister Exam

Other calculators:

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

Limit of the function x^3-4*x

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     / 3      \
 lim \x  - 4*x/
x->0+
lim⁡x→0+(x3−4x)\lim_{x \to 0^+}\left(x^{3} - 4 x\right) 
Limit(x^3 - 4*x, 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
02468-8-6-4-2-1010-20002000
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
One‐sided limits [src] 
     / 3      \
 lim \x  - 4*x/
x->0+
lim⁡x→0+(x3−4x)\lim_{x \to 0^+}\left(x^{3} - 4 x\right) 
0
00 
= 4.88092159433412e-31
     / 3      \
 lim \x  - 4*x/
x->0-
lim⁡x→0−(x3−4x)\lim_{x \to 0^-}\left(x^{3} - 4 x\right) 
0
00 
= -4.88092159433412e-31
= -4.88092159433412e-31
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(x3−4x)=0\lim_{x \to 0^-}\left(x^{3} - 4 x\right) = 0
More at x→0 from the left
lim⁡x→0+(x3−4x)=0\lim_{x \to 0^+}\left(x^{3} - 4 x\right) = 0
lim⁡x→∞(x3−4x)=∞\lim_{x \to \infty}\left(x^{3} - 4 x\right) = \infty
More at x→oo
lim⁡x→1−(x3−4x)=−3\lim_{x \to 1^-}\left(x^{3} - 4 x\right) = -3
More at x→1 from the left
lim⁡x→1+(x3−4x)=−3\lim_{x \to 1^+}\left(x^{3} - 4 x\right) = -3
More at x→1 from the right
lim⁡x→−∞(x3−4x)=−∞\lim_{x \to -\infty}\left(x^{3} - 4 x\right) = -\infty
More at x→-oo
Numerical answer [src] 
4.88092159433412e-31
4.88092159433412e-31
The graph
Limit of the function x^3-4*x
    © Mister Exam – Calculator