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Limit of the function
:
Limit of (1-2*x)^(1/x)
Limit of cos(x)/factorial(x)
Limit of sqrt(2)/2
Limit of cos(x)^4
sqrt(2)/2
Identical expressions
sqrt(two)/ two
square root of (2) divide by 2
square root of (two) divide by two
√(2)/2
sqrt2/2
sqrt(2) divide by 2
Similar expressions
sqrt(2)/(2*sqrt(x))
Limit of the function
/
sqrt(2)/2
Limit of the function sqrt(2)/2
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]
/ ___\ |\/ 2 | lim |-----| x->oo\ 2 /
lim
x
→
∞
(
2
2
)
\lim_{x \to \infty}\left(\frac{\sqrt{2}}{2}\right)
x
→
∞
lim
(
2
2
)
Limit(sqrt(2)/2, 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
-0.010
-0.008
-0.006
-0.004
-0.002
0.010
0.000
0.002
0.004
0.006
0.008
0.00
Plot the graph
Other limits x→0, -oo, +oo, 1
lim
x
→
∞
(
2
2
)
=
2
2
\lim_{x \to \infty}\left(\frac{\sqrt{2}}{2}\right) = \frac{\sqrt{2}}{2}
x
→
∞
lim
(
2
2
)
=
2
2
lim
x
→
0
−
(
2
2
)
=
2
2
\lim_{x \to 0^-}\left(\frac{\sqrt{2}}{2}\right) = \frac{\sqrt{2}}{2}
x
→
0
−
lim
(
2
2
)
=
2
2
More at x→0 from the left
lim
x
→
0
+
(
2
2
)
=
2
2
\lim_{x \to 0^+}\left(\frac{\sqrt{2}}{2}\right) = \frac{\sqrt{2}}{2}
x
→
0
+
lim
(
2
2
)
=
2
2
More at x→0 from the right
lim
x
→
1
−
(
2
2
)
=
2
2
\lim_{x \to 1^-}\left(\frac{\sqrt{2}}{2}\right) = \frac{\sqrt{2}}{2}
x
→
1
−
lim
(
2
2
)
=
2
2
More at x→1 from the left
lim
x
→
1
+
(
2
2
)
=
2
2
\lim_{x \to 1^+}\left(\frac{\sqrt{2}}{2}\right) = \frac{\sqrt{2}}{2}
x
→
1
+
lim
(
2
2
)
=
2
2
More at x→1 from the right
lim
x
→
−
∞
(
2
2
)
=
2
2
\lim_{x \to -\infty}\left(\frac{\sqrt{2}}{2}\right) = \frac{\sqrt{2}}{2}
x
→
−
∞
lim
(
2
2
)
=
2
2
More at x→-oo
Rapid solution
[src]
___ \/ 2 ----- 2
2
2
\frac{\sqrt{2}}{2}
2
2
Expand and simplify
The graph