Mister Exam

Other calculators:


2*cos(2*x)

Limit of the function 2*cos(2*x)

at
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src]
  lim   (2*cos(2*x))
   -pi              
x->----+            
    12              
limx(1)π12+(2cos(2x))\lim_{x \to \frac{\left(-1\right) \pi}{12}^+}\left(2 \cos{\left(2 x \right)}\right)
Limit(2*cos(2*x), x, (-pi)/12)
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
-0.50-0.40-0.30-0.20-0.100.000.100.200.300.400.5003
One‐sided limits [src]
  lim   (2*cos(2*x))
   -pi              
x->----+            
    12              
limx(1)π12+(2cos(2x))\lim_{x \to \frac{\left(-1\right) \pi}{12}^+}\left(2 \cos{\left(2 x \right)}\right)
  ___
\/ 3 
3\sqrt{3}
= 1.73205080756888
  lim   (2*cos(2*x))
   -pi              
x->-----            
    12              
limx(1)π12(2cos(2x))\lim_{x \to \frac{\left(-1\right) \pi}{12}^-}\left(2 \cos{\left(2 x \right)}\right)
  ___
\/ 3 
3\sqrt{3}
= 1.73205080756888
= 1.73205080756888
Rapid solution [src]
  ___
\/ 3 
3\sqrt{3}
Other limits x→0, -oo, +oo, 1
limx(1)π12(2cos(2x))=3\lim_{x \to \frac{\left(-1\right) \pi}{12}^-}\left(2 \cos{\left(2 x \right)}\right) = \sqrt{3}
More at x→(-pi)/12 from the left
limx(1)π12+(2cos(2x))=3\lim_{x \to \frac{\left(-1\right) \pi}{12}^+}\left(2 \cos{\left(2 x \right)}\right) = \sqrt{3}
limx(2cos(2x))=2,2\lim_{x \to \infty}\left(2 \cos{\left(2 x \right)}\right) = \left\langle -2, 2\right\rangle
More at x→oo
limx0(2cos(2x))=2\lim_{x \to 0^-}\left(2 \cos{\left(2 x \right)}\right) = 2
More at x→0 from the left
limx0+(2cos(2x))=2\lim_{x \to 0^+}\left(2 \cos{\left(2 x \right)}\right) = 2
More at x→0 from the right
limx1(2cos(2x))=2cos(2)\lim_{x \to 1^-}\left(2 \cos{\left(2 x \right)}\right) = 2 \cos{\left(2 \right)}
More at x→1 from the left
limx1+(2cos(2x))=2cos(2)\lim_{x \to 1^+}\left(2 \cos{\left(2 x \right)}\right) = 2 \cos{\left(2 \right)}
More at x→1 from the right
limx(2cos(2x))=2,2\lim_{x \to -\infty}\left(2 \cos{\left(2 x \right)}\right) = \left\langle -2, 2\right\rangle
More at x→-oo
Numerical answer [src]
1.73205080756888
1.73205080756888
The graph
Limit of the function 2*cos(2*x)