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cot(4*x)/sin(2*x)
Limit of the function/ cot(4*x)/sin(2*x)

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cot(4*x)/sin(2*x)

What you mean?

cot(4*x)/sin(2*x)
 
cot(4*x)/((sin(2)*x))
 
cot(4*x)*2*x/sin(x)
 
cot(4*x)/sin(2*x)
 
cot(4*x)/((sin(2)*x))
 
cot(4*x)*2*x/sin(x)
 
cot(4*x)*2*x/sin(x)

Limit of the function cot(4*x)/sin(2*x)

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The solution

You have entered [src] 
     /cot(4*x)\
 lim |--------|
x->0+\sin(2*x)/
lim⁡x→0+(cot⁡(4x)sin⁡(2x))\lim_{x \to 0^+}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) 
Limit(cot(4*x)/sin(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
02468-8-6-4-2-1010-50005000
Plot the graph
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(cot⁡(4x)sin⁡(2x))=∞\lim_{x \to 0^-}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \infty
More at x→0 from the left
lim⁡x→0+(cot⁡(4x)sin⁡(2x))=∞\lim_{x \to 0^+}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \infty
lim⁡x→∞(cot⁡(4x)sin⁡(2x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \left\langle -\infty, \infty\right\rangle
More at x→oo
lim⁡x→1−(cot⁡(4x)sin⁡(2x))=cot⁡(4)sin⁡(2)\lim_{x \to 1^-}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \frac{\cot{\left(4 \right)}}{\sin{\left(2 \right)}}
More at x→1 from the left
lim⁡x→1+(cot⁡(4x)sin⁡(2x))=cot⁡(4)sin⁡(2)\lim_{x \to 1^+}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \frac{\cot{\left(4 \right)}}{\sin{\left(2 \right)}}
More at x→1 from the right
lim⁡x→−∞(cot⁡(4x)sin⁡(2x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \left\langle -\infty, \infty\right\rangle
More at x→-oo
One‐sided limits [src] 
     /cot(4*x)\
 lim |--------|
x->0+\sin(2*x)/
lim⁡x→0+(cot⁡(4x)sin⁡(2x))\lim_{x \to 0^+}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) 
oo
∞\infty 
= 2849.54161768884
     /cot(4*x)\
 lim |--------|
x->0-\sin(2*x)/
lim⁡x→0−(cot⁡(4x)sin⁡(2x))\lim_{x \to 0^-}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) 
oo
∞\infty 
= 2849.54161768884
= 2849.54161768884
Numerical answer [src] 
2849.54161768884
2849.54161768884
The graph
Limit of the function cot(4*x)/sin(2*x)
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