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x*|x|
Limit of the function/ x*|x|

Limit of the function x*|x|

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The solution

You have entered [src] 
 lim (x*|x|)
x->0+
lim⁡x→0+(x∣x∣)\lim_{x \to 0^+}\left(x \left|{x}\right|\right) 
Limit(x*|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
02468-8-6-4-2-1010-200200
Plot the graph
One‐sided limits [src] 
 lim (x*|x|)
x->0+
lim⁡x→0+(x∣x∣)\lim_{x \to 0^+}\left(x \left|{x}\right|\right) 
0
00 
= -9.68305799950874e-32
 lim (x*|x|)
x->0-
lim⁡x→0−(x∣x∣)\lim_{x \to 0^-}\left(x \left|{x}\right|\right) 
0
00 
= 9.68305799950874e-32
= 9.68305799950874e-32
Rapid solution [src] 
0
00
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(x∣x∣)=0\lim_{x \to 0^-}\left(x \left|{x}\right|\right) = 0
More at x→0 from the left
lim⁡x→0+(x∣x∣)=0\lim_{x \to 0^+}\left(x \left|{x}\right|\right) = 0
lim⁡x→∞(x∣x∣)=∞\lim_{x \to \infty}\left(x \left|{x}\right|\right) = \infty
More at x→oo
lim⁡x→1−(x∣x∣)=1\lim_{x \to 1^-}\left(x \left|{x}\right|\right) = 1
More at x→1 from the left
lim⁡x→1+(x∣x∣)=1\lim_{x \to 1^+}\left(x \left|{x}\right|\right) = 1
More at x→1 from the right
lim⁡x→−∞(x∣x∣)=−∞\lim_{x \to -\infty}\left(x \left|{x}\right|\right) = -\infty
More at x→-oo
Numerical answer [src] 
-9.68305799950874e-32
-9.68305799950874e-32
The graph
Limit of the function x*|x|
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