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sin(2*x)/2
Limit of the function/ sin(2*x)/2

Limit of the function sin(2*x)/2

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The solution

You have entered [src] 
     /sin(2*x)\
 lim |--------|
x->0+\   2    /
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(2 x \right)}}{2}\right)$$ 
Limit(sin(2*x)/2, 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
One‐sided limits [src] 
     /sin(2*x)\
 lim |--------|
x->0+\   2    /
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(2 x \right)}}{2}\right)$$ 
0
$$0$$ 
= 1.01936700133329e-31
     /sin(2*x)\
 lim |--------|
x->0-\   2    /
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(2 x \right)}}{2}\right)$$ 
0
$$0$$ 
= -1.01936700133329e-31
= -1.01936700133329e-31
Rapid solution [src] 
0
$$0$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(2 x \right)}}{2}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(2 x \right)}}{2}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(2 x \right)}}{2}\right) = \left\langle - \frac{1}{2}, \frac{1}{2}\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(2 x \right)}}{2}\right) = \frac{\sin{\left(2 \right)}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(2 x \right)}}{2}\right) = \frac{\sin{\left(2 \right)}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(2 x \right)}}{2}\right) = \left\langle - \frac{1}{2}, \frac{1}{2}\right\rangle$$
More at x→-oo
Numerical answer [src] 
1.01936700133329e-31
1.01936700133329e-31
The graph
Limit of the function sin(2*x)/2
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