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sqrt(x)*sin(x)
Limit of the function/ sqrt(x)*sin(x)

Limit of the function sqrt(x)*sin(x)

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     /  ___       \
 lim \\/ x *sin(x)/
x->0+
lim⁡x→0+(xsin⁡(x))\lim_{x \to 0^+}\left(\sqrt{x} \sin{\left(x \right)}\right) 
Limit(sqrt(x)*sin(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
02468-8-6-4-2-10105-5
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(xsin⁡(x))=0\lim_{x \to 0^-}\left(\sqrt{x} \sin{\left(x \right)}\right) = 0
More at x→0 from the left
lim⁡x→0+(xsin⁡(x))=0\lim_{x \to 0^+}\left(\sqrt{x} \sin{\left(x \right)}\right) = 0
lim⁡x→∞(xsin⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(\sqrt{x} \sin{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
More at x→oo
lim⁡x→1−(xsin⁡(x))=sin⁡(1)\lim_{x \to 1^-}\left(\sqrt{x} \sin{\left(x \right)}\right) = \sin{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+(xsin⁡(x))=sin⁡(1)\lim_{x \to 1^+}\left(\sqrt{x} \sin{\left(x \right)}\right) = \sin{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞(xsin⁡(x))=i⟨−∞,∞⟩\lim_{x \to -\infty}\left(\sqrt{x} \sin{\left(x \right)}\right) = i \left\langle -\infty, \infty\right\rangle
More at x→-oo
Rapid solution [src] 
0
00
Expand and simplify
One‐sided limits [src] 
     /  ___       \
 lim \\/ x *sin(x)/
x->0+
lim⁡x→0+(xsin⁡(x))\lim_{x \to 0^+}\left(\sqrt{x} \sin{\left(x \right)}\right) 
0
00 
= 4.84193210180299e-6
     /  ___       \
 lim \\/ x *sin(x)/
x->0-
lim⁡x→0−(xsin⁡(x))\lim_{x \to 0^-}\left(\sqrt{x} \sin{\left(x \right)}\right) 
0
00 
= (0.0 - 4.84193210180299e-6j)
= (0.0 - 4.84193210180299e-6j)
Numerical answer [src] 
4.84193210180299e-6
4.84193210180299e-6
The graph
Limit of the function sqrt(x)*sin(x)
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