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Limit of the function
:
Limit of cot(5*pi*x)*log(x)
Limit of pi-2*acot(x)/(-1+e^(3/x))
Limit of log(1+2^x)*log(1+3/x)
Limit of n/factorial(n)
Derivative of
:
z^4
Graphing y =
:
z^4
z^4
Identical expressions
z^ four
z to the power of 4
z to the power of four
z4
z⁴
Limit of the function
/
z^4
Limit of the function z^4
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]
4 lim z z->-1+
lim
z
→
−
1
+
z
4
\lim_{z \to -1^+} z^{4}
z
→
−
1
+
lim
z
4
Limit(z^4, z, -1)
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
-2.0
-1.5
-1.0
-0.5
2.0
0.0
0.5
1.0
1.5
0
20
Plot the graph
Rapid solution
[src]
1
1
1
1
Expand and simplify
Other limits z→0, -oo, +oo, 1
lim
z
→
−
1
−
z
4
=
1
\lim_{z \to -1^-} z^{4} = 1
z
→
−
1
−
lim
z
4
=
1
More at z→-1 from the left
lim
z
→
−
1
+
z
4
=
1
\lim_{z \to -1^+} z^{4} = 1
z
→
−
1
+
lim
z
4
=
1
lim
z
→
∞
z
4
=
∞
\lim_{z \to \infty} z^{4} = \infty
z
→
∞
lim
z
4
=
∞
More at z→oo
lim
z
→
0
−
z
4
=
0
\lim_{z \to 0^-} z^{4} = 0
z
→
0
−
lim
z
4
=
0
More at z→0 from the left
lim
z
→
0
+
z
4
=
0
\lim_{z \to 0^+} z^{4} = 0
z
→
0
+
lim
z
4
=
0
More at z→0 from the right
lim
z
→
1
−
z
4
=
1
\lim_{z \to 1^-} z^{4} = 1
z
→
1
−
lim
z
4
=
1
More at z→1 from the left
lim
z
→
1
+
z
4
=
1
\lim_{z \to 1^+} z^{4} = 1
z
→
1
+
lim
z
4
=
1
More at z→1 from the right
lim
z
→
−
∞
z
4
=
∞
\lim_{z \to -\infty} z^{4} = \infty
z
→
−
∞
lim
z
4
=
∞
More at z→-oo
One‐sided limits
[src]
4 lim z z->-1+
lim
z
→
−
1
+
z
4
\lim_{z \to -1^+} z^{4}
z
→
−
1
+
lim
z
4
1
1
1
1
= 1.0
4 lim z z->-1-
lim
z
→
−
1
−
z
4
\lim_{z \to -1^-} z^{4}
z
→
−
1
−
lim
z
4
1
1
1
1
= 1.0
= 1.0
Numerical answer
[src]
1.0
1.0
The graph