Mister Exam

Other calculators:

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

Limit of the function sin(2*x)

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 lim sin(2*x)
x->0+
lim⁡x→0+sin⁡(2x)\lim_{x \to 0^+} \sin{\left(2 x \right)} 
Limit(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
02468-8-6-4-2-10102-2
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→0−sin⁡(2x)=0\lim_{x \to 0^-} \sin{\left(2 x \right)} = 0
More at x→0 from the left
lim⁡x→0+sin⁡(2x)=0\lim_{x \to 0^+} \sin{\left(2 x \right)} = 0
lim⁡x→∞sin⁡(2x)=⟨−1,1⟩\lim_{x \to \infty} \sin{\left(2 x \right)} = \left\langle -1, 1\right\rangle
More at x→oo
lim⁡x→1−sin⁡(2x)=sin⁡(2)\lim_{x \to 1^-} \sin{\left(2 x \right)} = \sin{\left(2 \right)}
More at x→1 from the left
lim⁡x→1+sin⁡(2x)=sin⁡(2)\lim_{x \to 1^+} \sin{\left(2 x \right)} = \sin{\left(2 \right)}
More at x→1 from the right
lim⁡x→−∞sin⁡(2x)=⟨−1,1⟩\lim_{x \to -\infty} \sin{\left(2 x \right)} = \left\langle -1, 1\right\rangle
More at x→-oo
One‐sided limits [src] 
 lim sin(2*x)
x->0+
lim⁡x→0+sin⁡(2x)\lim_{x \to 0^+} \sin{\left(2 x \right)} 
0
00 
= 2.03873400266658e-31
 lim sin(2*x)
x->0-
lim⁡x→0−sin⁡(2x)\lim_{x \to 0^-} \sin{\left(2 x \right)} 
0
00 
= -2.03873400266658e-31
= -2.03873400266658e-31
Numerical answer [src] 
2.03873400266658e-31
2.03873400266658e-31
The graph
Limit of the function sin(2*x)
    © Mister Exam – Calculator