Mister Exam

Other calculators:

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

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

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     /  4*x   \
 lim |--------|
x->oo\sin(2*x)/
lim⁡x→∞(4xsin⁡(2x))\lim_{x \to \infty}\left(\frac{4 x}{\sin{\left(2 x \right)}}\right) 
Limit((4*x)/sin(2*x), x, oo, dir='-')
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
02468-8-6-4-2-1010-10001000
Plot the graph
Rapid solution [src] 
     /  4*x   \
 lim |--------|
x->oo\sin(2*x)/
lim⁡x→∞(4xsin⁡(2x))\lim_{x \to \infty}\left(\frac{4 x}{\sin{\left(2 x \right)}}\right)
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(4xsin⁡(2x))\lim_{x \to \infty}\left(\frac{4 x}{\sin{\left(2 x \right)}}\right)
lim⁡x→0−(4xsin⁡(2x))=2\lim_{x \to 0^-}\left(\frac{4 x}{\sin{\left(2 x \right)}}\right) = 2
More at x→0 from the left
lim⁡x→0+(4xsin⁡(2x))=2\lim_{x \to 0^+}\left(\frac{4 x}{\sin{\left(2 x \right)}}\right) = 2
More at x→0 from the right
lim⁡x→1−(4xsin⁡(2x))=4sin⁡(2)\lim_{x \to 1^-}\left(\frac{4 x}{\sin{\left(2 x \right)}}\right) = \frac{4}{\sin{\left(2 \right)}}
More at x→1 from the left
lim⁡x→1+(4xsin⁡(2x))=4sin⁡(2)\lim_{x \to 1^+}\left(\frac{4 x}{\sin{\left(2 x \right)}}\right) = \frac{4}{\sin{\left(2 \right)}}
More at x→1 from the right
lim⁡x→−∞(4xsin⁡(2x))\lim_{x \to -\infty}\left(\frac{4 x}{\sin{\left(2 x \right)}}\right)
More at x→-oo
The graph
Limit of the function 4*x/sin(2*x)
    © Mister Exam – Calculator