Mister Exam
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How to use it?
Limit of the function
:
Limit of log(log(x))
Limit of sin(factorial(x))
Limit of sqrt(x)*log(x)
Limit of sin(sqrt(x))/sqrt(x)
Derivative of
:
log(log(x))
Identical expressions
log(log(x))
logarithm of ( logarithm of (x))
loglogx
Limit of the function
/
log(log(x))
Limit of the function log(log(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 log(log(x)) x->-oo
lim
x
→
−
∞
log
(
log
(
x
)
)
\lim_{x \to -\infty} \log{\left(\log{\left(x \right)} \right)}
x
→
−
∞
lim
lo
g
(
lo
g
(
x
)
)
Limit(log(log(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
5
-5
Plot the graph
Rapid solution
[src]
oo
∞
\infty
∞
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim
x
→
−
∞
log
(
log
(
x
)
)
=
∞
\lim_{x \to -\infty} \log{\left(\log{\left(x \right)} \right)} = \infty
x
→
−
∞
lim
lo
g
(
lo
g
(
x
)
)
=
∞
lim
x
→
∞
log
(
log
(
x
)
)
=
∞
\lim_{x \to \infty} \log{\left(\log{\left(x \right)} \right)} = \infty
x
→
∞
lim
lo
g
(
lo
g
(
x
)
)
=
∞
More at x→oo
lim
x
→
0
−
log
(
log
(
x
)
)
=
∞
\lim_{x \to 0^-} \log{\left(\log{\left(x \right)} \right)} = \infty
x
→
0
−
lim
lo
g
(
lo
g
(
x
)
)
=
∞
More at x→0 from the left
lim
x
→
0
+
log
(
log
(
x
)
)
=
∞
\lim_{x \to 0^+} \log{\left(\log{\left(x \right)} \right)} = \infty
x
→
0
+
lim
lo
g
(
lo
g
(
x
)
)
=
∞
More at x→0 from the right
lim
x
→
1
−
log
(
log
(
x
)
)
=
−
∞
\lim_{x \to 1^-} \log{\left(\log{\left(x \right)} \right)} = -\infty
x
→
1
−
lim
lo
g
(
lo
g
(
x
)
)
=
−
∞
More at x→1 from the left
lim
x
→
1
+
log
(
log
(
x
)
)
=
−
∞
\lim_{x \to 1^+} \log{\left(\log{\left(x \right)} \right)} = -\infty
x
→
1
+
lim
lo
g
(
lo
g
(
x
)
)
=
−
∞
More at x→1 from the right
The graph