Mister Exam

Other calculators:

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

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

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     /  sin(x)  \
 lim |----------|
x->0+\1 + cos(x)/
lim⁡x→0+(sin⁡(x)cos⁡(x)+1)\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
02468-8-6-4-2-1010-500500
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
One‐sided limits [src] 
     /  sin(x)  \
 lim |----------|
x->0+\1 + cos(x)/
lim⁡x→0+(sin⁡(x)cos⁡(x)+1)\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right) 
0
00 
= 4.95349509297983e-32
     /  sin(x)  \
 lim |----------|
x->0-\1 + cos(x)/
lim⁡x→0−(sin⁡(x)cos⁡(x)+1)\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right) 
0
00 
= -4.95349509297983e-32
= -4.95349509297983e-32
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(sin⁡(x)cos⁡(x)+1)=0\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→0+(sin⁡(x)cos⁡(x)+1)=0\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right) = 0
lim⁡x→∞(sin⁡(x)cos⁡(x)+1)\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)
More at x→oo
lim⁡x→1−(sin⁡(x)cos⁡(x)+1)=sin⁡(1)cos⁡(1)+1\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→1+(sin⁡(x)cos⁡(x)+1)=sin⁡(1)cos⁡(1)+1\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→−∞(sin⁡(x)cos⁡(x)+1)\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))
    © Mister Exam – Calculator