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

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

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You have entered [src] 
     /cos(x)\
 lim |------|
x->0+\sin(x)/
lim⁡x→0+(cos⁡(x)sin⁡(x))\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) 
Limit(cos(x)/sin(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
02468-8-6-4-2-1010-250250
Plot the graph
One‐sided limits [src] 
     /cos(x)\
 lim |------|
x->0+\sin(x)/
lim⁡x→0+(cos⁡(x)sin⁡(x))\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) 
oo
∞\infty 
= 150.997792488027
     /cos(x)\
 lim |------|
x->0-\sin(x)/
lim⁡x→0−(cos⁡(x)sin⁡(x))\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) 
-oo
−∞-\infty 
= -150.997792488027
= -150.997792488027
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(cos⁡(x)sin⁡(x))=∞\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) = \infty
More at x→0 from the left
lim⁡x→0+(cos⁡(x)sin⁡(x))=∞\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) = \infty
lim⁡x→∞(cos⁡(x)sin⁡(x))\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)
More at x→oo
lim⁡x→1−(cos⁡(x)sin⁡(x))=cos⁡(1)sin⁡(1)\lim_{x \to 1^-}\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) = \frac{\cos{\left(1 \right)}}{\sin{\left(1 \right)}}
More at x→1 from the left
lim⁡x→1+(cos⁡(x)sin⁡(x))=cos⁡(1)sin⁡(1)\lim_{x \to 1^+}\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) = \frac{\cos{\left(1 \right)}}{\sin{\left(1 \right)}}
More at x→1 from the right
lim⁡x→−∞(cos⁡(x)sin⁡(x))\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)
More at x→-oo
Numerical answer [src] 
150.997792488027
150.997792488027
The graph
Limit of the function cos(x)/sin(x)
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