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

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

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     / 3    /1\\
 lim |x *sin|-||
x->0+\      \x//
lim⁡x→0+(x3sin⁡(1x))\lim_{x \to 0^+}\left(x^{3} \sin{\left(\frac{1}{x} \right)}\right) 
Limit(x^3*sin(1/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
02468-8-6-4-2-1010200-100
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(x3sin⁡(1x))=0\lim_{x \to 0^-}\left(x^{3} \sin{\left(\frac{1}{x} \right)}\right) = 0
More at x→0 from the left
lim⁡x→0+(x3sin⁡(1x))=0\lim_{x \to 0^+}\left(x^{3} \sin{\left(\frac{1}{x} \right)}\right) = 0
lim⁡x→∞(x3sin⁡(1x))=∞\lim_{x \to \infty}\left(x^{3} \sin{\left(\frac{1}{x} \right)}\right) = \infty
More at x→oo
lim⁡x→1−(x3sin⁡(1x))=sin⁡(1)\lim_{x \to 1^-}\left(x^{3} \sin{\left(\frac{1}{x} \right)}\right) = \sin{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+(x3sin⁡(1x))=sin⁡(1)\lim_{x \to 1^+}\left(x^{3} \sin{\left(\frac{1}{x} \right)}\right) = \sin{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞(x3sin⁡(1x))=∞\lim_{x \to -\infty}\left(x^{3} \sin{\left(\frac{1}{x} \right)}\right) = \infty
More at x→-oo
Rapid solution [src] 
0
00
Expand and simplify
One‐sided limits [src] 
     / 3    /1\\
 lim |x *sin|-||
x->0+\      \x//
lim⁡x→0+(x3sin⁡(1x))\lim_{x \to 0^+}\left(x^{3} \sin{\left(\frac{1}{x} \right)}\right) 
0
00 
= -1.57993404767779e-19
     / 3    /1\\
 lim |x *sin|-||
x->0-\      \x//
lim⁡x→0−(x3sin⁡(1x))\lim_{x \to 0^-}\left(x^{3} \sin{\left(\frac{1}{x} \right)}\right) 
0
00 
= -1.57993404767779e-19
= -1.57993404767779e-19
Numerical answer [src] 
-1.57993404767779e-19
-1.57993404767779e-19
The graph
Limit of the function x^3*sin(1/x)
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