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x*log(x)^2
Limit of the function/ x*log(x)^2

Limit of the function x*log(x)^2

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     /     2   \
 lim \x*log (x)/
x->0+
lim⁡x→0+(xlog⁡(x)2)\lim_{x \to 0^+}\left(x \log{\left(x \right)}^{2}\right) 
Limit(x*log(x)^2, x, 0)
The graph
02468-8-6-4-2-10100100
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Rapid solution [src] 
0
00
Expand and simplify
One‐sided limits [src] 
     /     2   \
 lim \x*log (x)/
x->0+
lim⁡x→0+(xlog⁡(x)2)\lim_{x \to 0^+}\left(x \log{\left(x \right)}^{2}\right) 
0
00 
= 0.0145268477491906
     /     2   \
 lim \x*log (x)/
x->0-
lim⁡x→0−(xlog⁡(x)2)\lim_{x \to 0^-}\left(x \log{\left(x \right)}^{2}\right) 
0
00 
= (-0.0126046545241533 + 0.0122434670558655j)
= (-0.0126046545241533 + 0.0122434670558655j)
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(xlog⁡(x)2)=0\lim_{x \to 0^-}\left(x \log{\left(x \right)}^{2}\right) = 0
More at x→0 from the left
lim⁡x→0+(xlog⁡(x)2)=0\lim_{x \to 0^+}\left(x \log{\left(x \right)}^{2}\right) = 0
lim⁡x→∞(xlog⁡(x)2)=∞\lim_{x \to \infty}\left(x \log{\left(x \right)}^{2}\right) = \infty
More at x→oo
lim⁡x→1−(xlog⁡(x)2)=0\lim_{x \to 1^-}\left(x \log{\left(x \right)}^{2}\right) = 0
More at x→1 from the left
lim⁡x→1+(xlog⁡(x)2)=0\lim_{x \to 1^+}\left(x \log{\left(x \right)}^{2}\right) = 0
More at x→1 from the right
lim⁡x→−∞(xlog⁡(x)2)=−∞\lim_{x \to -\infty}\left(x \log{\left(x \right)}^{2}\right) = -\infty
More at x→-oo
Numerical answer [src] 
0.0145268477491906
0.0145268477491906
The graph
Limit of the function x*log(x)^2
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