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

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

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     /cos(2*x)\
 lim |--------|
x->0+\   2    /
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(2 x \right)}}{2}\right)$$ 
Limit(cos(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] 
     /cos(2*x)\
 lim |--------|
x->0+\   2    /
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(2 x \right)}}{2}\right)$$ 
1/2
$$\frac{1}{2}$$ 
= 0.5
     /cos(2*x)\
 lim |--------|
x->0-\   2    /
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(2 x \right)}}{2}\right)$$ 
1/2
$$\frac{1}{2}$$ 
= 0.5
= 0.5
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(2 x \right)}}{2}\right) = \frac{1}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(2 x \right)}}{2}\right) = \frac{1}{2}$$
$$\lim_{x \to \infty}\left(\frac{\cos{\left(2 x \right)}}{2}\right) = \left\langle - \frac{1}{2}, \frac{1}{2}\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\cos{\left(2 x \right)}}{2}\right) = \frac{\cos{\left(2 \right)}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos{\left(2 x \right)}}{2}\right) = \frac{\cos{\left(2 \right)}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos{\left(2 x \right)}}{2}\right) = \left\langle - \frac{1}{2}, \frac{1}{2}\right\rangle$$
More at x→-oo
Rapid solution [src] 
1/2
$$\frac{1}{2}$$
Expand and simplify
Numerical answer [src] 
0.5
0.5
The graph
Limit of the function cos(2*x)/2
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