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1-cos(2*x)
Limit of the function/ 1-cos(2*x)

Limit of the function 1-cos(2*x)

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You have entered [src] 
 lim (1 - cos(2*x))
x->0+
$$\lim_{x \to 0^+}\left(1 - \cos{\left(2 x \right)}\right)$$ 
Limit(1 - cos(2*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
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Rapid solution [src] 
0
$$0$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(1 - \cos{\left(2 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(1 - \cos{\left(2 x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(1 - \cos{\left(2 x \right)}\right) = \left\langle 0, 2\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(1 - \cos{\left(2 x \right)}\right) = 1 - \cos{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(1 - \cos{\left(2 x \right)}\right) = 1 - \cos{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(1 - \cos{\left(2 x \right)}\right) = \left\langle 0, 2\right\rangle$$
More at x→-oo
One‐sided limits [src] 
 lim (1 - cos(2*x))
x->0+
$$\lim_{x \to 0^+}\left(1 - \cos{\left(2 x \right)}\right)$$ 
0
$$0$$ 
= 3.69697164723554e-31
 lim (1 - cos(2*x))
x->0-
$$\lim_{x \to 0^-}\left(1 - \cos{\left(2 x \right)}\right)$$ 
0
$$0$$ 
= 3.69697164723554e-31
= 3.69697164723554e-31
Numerical answer [src] 
3.69697164723554e-31
3.69697164723554e-31
The graph
Limit of the function 1-cos(2*x)
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