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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+
$$\lim_{x \to 0^+}\left(\sqrt{x} \sin{\left(x \right)}\right)$$ 
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
Plot the graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\sqrt{x} \sin{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sqrt{x} \sin{\left(x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(\sqrt{x} \sin{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\sqrt{x} \sin{\left(x \right)}\right) = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sqrt{x} \sin{\left(x \right)}\right) = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sqrt{x} \sin{\left(x \right)}\right) = i \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
Rapid solution [src] 
0
$$0$$
Expand and simplify
One‐sided limits [src] 
     /  ___       \
 lim \\/ x *sin(x)/
x->0+
$$\lim_{x \to 0^+}\left(\sqrt{x} \sin{\left(x \right)}\right)$$ 
0
$$0$$ 
= 4.84193210180299e-6
     /  ___       \
 lim \\/ x *sin(x)/
x->0-
$$\lim_{x \to 0^-}\left(\sqrt{x} \sin{\left(x \right)}\right)$$ 
0
$$0$$ 
= (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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