Mister Exam
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How to use it?
Limit of the function
:
Limit of x^2*(1/3-cos(8*x)/3)
Limit of (-9-x)/(-2+x)
Limit of x^(4/x)
Limit of (-2+x^2-x)/(-2+x+3*x^2)
Derivative of
:
(1/2)^x
Integral of d{x}
:
(1/2)^x
Graphing y =
:
(1/2)^x
Identical expressions
(one / two)^x
(1 divide by 2) to the power of x
(one divide by two) to the power of x
(1/2)x
1/2x
1/2^x
(1 divide by 2)^x
Limit of the function
/
(1/2)^x
Limit of the function (1/2)^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]
-x lim 2 x->oo
lim
x
→
∞
(
1
2
)
x
\lim_{x \to \infty} \left(\frac{1}{2}\right)^{x}
x
→
∞
lim
(
2
1
)
x
Limit((1/2)^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
0
1000
Plot the graph
Other limits x→0, -oo, +oo, 1
lim
x
→
∞
(
1
2
)
x
=
0
\lim_{x \to \infty} \left(\frac{1}{2}\right)^{x} = 0
x
→
∞
lim
(
2
1
)
x
=
0
lim
x
→
0
−
(
1
2
)
x
=
1
\lim_{x \to 0^-} \left(\frac{1}{2}\right)^{x} = 1
x
→
0
−
lim
(
2
1
)
x
=
1
More at x→0 from the left
lim
x
→
0
+
(
1
2
)
x
=
1
\lim_{x \to 0^+} \left(\frac{1}{2}\right)^{x} = 1
x
→
0
+
lim
(
2
1
)
x
=
1
More at x→0 from the right
lim
x
→
1
−
(
1
2
)
x
=
1
2
\lim_{x \to 1^-} \left(\frac{1}{2}\right)^{x} = \frac{1}{2}
x
→
1
−
lim
(
2
1
)
x
=
2
1
More at x→1 from the left
lim
x
→
1
+
(
1
2
)
x
=
1
2
\lim_{x \to 1^+} \left(\frac{1}{2}\right)^{x} = \frac{1}{2}
x
→
1
+
lim
(
2
1
)
x
=
2
1
More at x→1 from the right
lim
x
→
−
∞
(
1
2
)
x
=
∞
\lim_{x \to -\infty} \left(\frac{1}{2}\right)^{x} = \infty
x
→
−
∞
lim
(
2
1
)
x
=
∞
More at x→-oo
Rapid solution
[src]
0
0
0
0
Expand and simplify
The graph