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Limit of the function
:
Limit of (-1+x)/log(x)
Limit of (-1+e^(3*x))/x
Limit of (-1+e^x)/sin(x)
Limit of (1+e^x)^(1/x)
Derivative of
:
2*sin(2*x)
Graphing y =
:
2*sin(2*x)
Integral of d{x}
:
2*sin(2*x)
Identical expressions
two *sin(two *x)
2 multiply by sinus of (2 multiply by x)
two multiply by sinus of (two multiply by x)
2sin(2x)
2sin2x
Limit of the function
/
2*sin(2*x)
Limit of the function 2*sin(2*x)
at
→
Calculate the limit!
v
For end points:
---------
From the left (x0-)
From the right (x0+)
The graph:
from
to
Piecewise:
{
enter the piecewise function here
The solution
You have entered
[src]
lim (2*sin(2*x)) x->oo
lim
x
→
∞
(
2
sin
(
2
x
)
)
\lim_{x \to \infty}\left(2 \sin{\left(2 x \right)}\right)
x
→
∞
lim
(
2
sin
(
2
x
)
)
Limit(2*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
0
2
4
6
8
-8
-6
-4
-2
-10
10
5
-5
Plot the graph
Other limits x→0, -oo, +oo, 1
lim
x
→
∞
(
2
sin
(
2
x
)
)
=
⟨
−
2
,
2
⟩
\lim_{x \to \infty}\left(2 \sin{\left(2 x \right)}\right) = \left\langle -2, 2\right\rangle
x
→
∞
lim
(
2
sin
(
2
x
)
)
=
⟨
−
2
,
2
⟩
lim
x
→
0
−
(
2
sin
(
2
x
)
)
=
0
\lim_{x \to 0^-}\left(2 \sin{\left(2 x \right)}\right) = 0
x
→
0
−
lim
(
2
sin
(
2
x
)
)
=
0
More at x→0 from the left
lim
x
→
0
+
(
2
sin
(
2
x
)
)
=
0
\lim_{x \to 0^+}\left(2 \sin{\left(2 x \right)}\right) = 0
x
→
0
+
lim
(
2
sin
(
2
x
)
)
=
0
More at x→0 from the right
lim
x
→
1
−
(
2
sin
(
2
x
)
)
=
2
sin
(
2
)
\lim_{x \to 1^-}\left(2 \sin{\left(2 x \right)}\right) = 2 \sin{\left(2 \right)}
x
→
1
−
lim
(
2
sin
(
2
x
)
)
=
2
sin
(
2
)
More at x→1 from the left
lim
x
→
1
+
(
2
sin
(
2
x
)
)
=
2
sin
(
2
)
\lim_{x \to 1^+}\left(2 \sin{\left(2 x \right)}\right) = 2 \sin{\left(2 \right)}
x
→
1
+
lim
(
2
sin
(
2
x
)
)
=
2
sin
(
2
)
More at x→1 from the right
lim
x
→
−
∞
(
2
sin
(
2
x
)
)
=
⟨
−
2
,
2
⟩
\lim_{x \to -\infty}\left(2 \sin{\left(2 x \right)}\right) = \left\langle -2, 2\right\rangle
x
→
−
∞
lim
(
2
sin
(
2
x
)
)
=
⟨
−
2
,
2
⟩
More at x→-oo
Rapid solution
[src]
<-2, 2>
⟨
−
2
,
2
⟩
\left\langle -2, 2\right\rangle
⟨
−
2
,
2
⟩
Expand and simplify
The graph