Mister Exam
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How to use it?
Limit of the function
:
Limit of (-2*sin(a+x)+sin(a)+sin(a+2*x))/x^2
Limit of tan(8*x)/(5*x)
Limit of log(tan(x))*tan(x)
Limit of cos(x)^2/x
Identical expressions
cos(x)^ two /x
co sinus of e of (x) squared divide by x
co sinus of e of (x) to the power of two divide by x
cos(x)2/x
cosx2/x
cos(x)²/x
cos(x) to the power of 2/x
cosx^2/x
cos(x)^2 divide by x
Similar expressions
(1-cos(x^2))/x^2
cos(x)^2/(x-pi/2)
(1-cos(x))^2/x^4
cosx^2/x
What you mean?
cos(x)^2/x
cos(x)^(2/x)
cos(x)^(2/x)
Limit of the function
/
cos(x)^2/x
You entered:
cos(x)^2/x
What you mean?
cos(x)^2/x
Choose
cos(x)^(2/x)
Choose
cos(x)^(2/x)
Choose
Limit of the function cos(x)^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]
/ 2 \ |cos (x)| lim |-------| x->oo\ x /
lim
x
→
∞
(
cos
2
(
x
)
x
)
\lim_{x \to \infty}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right)
x
→
∞
lim
(
x
cos
2
(
x
)
)
Limit(cos(x)^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
-20
20
Plot the graph
Rapid solution
[src]
0
0
0
0
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim
x
→
∞
(
cos
2
(
x
)
x
)
=
0
\lim_{x \to \infty}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = 0
x
→
∞
lim
(
x
cos
2
(
x
)
)
=
0
lim
x
→
0
−
(
cos
2
(
x
)
x
)
=
−
∞
\lim_{x \to 0^-}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = -\infty
x
→
0
−
lim
(
x
cos
2
(
x
)
)
=
−
∞
More at x→0 from the left
lim
x
→
0
+
(
cos
2
(
x
)
x
)
=
∞
\lim_{x \to 0^+}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = \infty
x
→
0
+
lim
(
x
cos
2
(
x
)
)
=
∞
More at x→0 from the right
lim
x
→
1
−
(
cos
2
(
x
)
x
)
=
cos
2
(
1
)
\lim_{x \to 1^-}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = \cos^{2}{\left(1 \right)}
x
→
1
−
lim
(
x
cos
2
(
x
)
)
=
cos
2
(
1
)
More at x→1 from the left
lim
x
→
1
+
(
cos
2
(
x
)
x
)
=
cos
2
(
1
)
\lim_{x \to 1^+}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = \cos^{2}{\left(1 \right)}
x
→
1
+
lim
(
x
cos
2
(
x
)
)
=
cos
2
(
1
)
More at x→1 from the right
lim
x
→
−
∞
(
cos
2
(
x
)
x
)
=
0
\lim_{x \to -\infty}\left(\frac{\cos^{2}{\left(x \right)}}{x}\right) = 0
x
→
−
∞
lim
(
x
cos
2
(
x
)
)
=
0
More at x→-oo
The graph