Mister Exam

Other calculators:


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

You entered:

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

What you mean?

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

at
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src]
     /cot(4*x)\
 lim |--------|
x->0+\sin(2*x)/
limx0+(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
Rapid solution [src]
oo
\infty
Other limits x→0, -oo, +oo, 1
limx0(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
limx0+(cot(4x)sin(2x))=\lim_{x \to 0^+}\left(\frac{\cot{\left(4 x \right)}}{\sin{\left(2 x \right)}}\right) = \infty
limx(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
limx1(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
limx1+(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
limx(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)/
limx0+(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)/
limx0(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)