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sin(x)/(1+cos(x))
Limit of the function/ sin(x)/(1+cos(x))

Limit of the function sin(x)/(1+cos(x))

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     /  sin(x)  \
 lim |----------|
x->0+\1 + cos(x)/
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)$$ 
Limit(sin(x)/(1 + cos(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
Rapid solution [src] 
0
$$0$$
Expand and simplify
One‐sided limits [src] 
     /  sin(x)  \
 lim |----------|
x->0+\1 + cos(x)/
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)$$ 
0
$$0$$ 
= 4.95349509297983e-32
     /  sin(x)  \
 lim |----------|
x->0-\1 + cos(x)/
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)$$ 
0
$$0$$ 
= -4.95349509297983e-32
= -4.95349509297983e-32
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right) = \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)} + 1}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right) = \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)} + 1}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)$$
More at x→-oo
Numerical answer [src] 
4.95349509297983e-32
4.95349509297983e-32
The graph
Limit of the function sin(x)/(1+cos(x))
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