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Limit of the function
:
Limit of (-1+x)/(-1+x^3)
Limit of n2*(5/2+n/2)
Limit of (3+x^2-4*x)/(-9+x^2)
Limit of (-3+sqrt(1+4*x))/(-8+x^3)
Integral of d{x}
:
x*sin(2*x)
Derivative of
:
x*sin(2*x)
Identical expressions
x*sin(two *x)
x multiply by sinus of (2 multiply by x)
x multiply by sinus of (two multiply by x)
xsin(2x)
xsin2x
Similar expressions
e^(-x)*sin(2*x)
x^sin(2*x)
x*(sin(2*x)/6+sin(4*x)/6)
cot(7*x)*sin(2*x)
Limit of the function
/
x*sin(2*x)
Limit of the function x*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 (x*sin(2*x)) x->-oo
lim
x
→
−
∞
(
x
sin
(
2
x
)
)
\lim_{x \to -\infty}\left(x \sin{\left(2 x \right)}\right)
x
→
−
∞
lim
(
x
sin
(
2
x
)
)
Limit(x*sin(2*x), x, -oo)
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
-20
20
Plot the graph
Rapid solution
[src]
-oo*sign(<-1, 1>)
−
∞
sign
(
⟨
−
1
,
1
⟩
)
- \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
−
∞
sign
(
⟨
−
1
,
1
⟩
)
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim
x
→
−
∞
(
x
sin
(
2
x
)
)
=
−
∞
sign
(
⟨
−
1
,
1
⟩
)
\lim_{x \to -\infty}\left(x \sin{\left(2 x \right)}\right) = - \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
x
→
−
∞
lim
(
x
sin
(
2
x
)
)
=
−
∞
sign
(
⟨
−
1
,
1
⟩
)
lim
x
→
∞
(
x
sin
(
2
x
)
)
=
∞
sign
(
⟨
−
1
,
1
⟩
)
\lim_{x \to \infty}\left(x \sin{\left(2 x \right)}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
x
→
∞
lim
(
x
sin
(
2
x
)
)
=
∞
sign
(
⟨
−
1
,
1
⟩
)
More at x→oo
lim
x
→
0
−
(
x
sin
(
2
x
)
)
=
0
\lim_{x \to 0^-}\left(x \sin{\left(2 x \right)}\right) = 0
x
→
0
−
lim
(
x
sin
(
2
x
)
)
=
0
More at x→0 from the left
lim
x
→
0
+
(
x
sin
(
2
x
)
)
=
0
\lim_{x \to 0^+}\left(x \sin{\left(2 x \right)}\right) = 0
x
→
0
+
lim
(
x
sin
(
2
x
)
)
=
0
More at x→0 from the right
lim
x
→
1
−
(
x
sin
(
2
x
)
)
=
sin
(
2
)
\lim_{x \to 1^-}\left(x \sin{\left(2 x \right)}\right) = \sin{\left(2 \right)}
x
→
1
−
lim
(
x
sin
(
2
x
)
)
=
sin
(
2
)
More at x→1 from the left
lim
x
→
1
+
(
x
sin
(
2
x
)
)
=
sin
(
2
)
\lim_{x \to 1^+}\left(x \sin{\left(2 x \right)}\right) = \sin{\left(2 \right)}
x
→
1
+
lim
(
x
sin
(
2
x
)
)
=
sin
(
2
)
More at x→1 from the right
The graph