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Limit of the function
:
Limit of (5-5*x)/(-1+sqrt(x))
Limit of ((-4+3*x)/(2+3*x))^(2*x)
Limit of (3+x^2-4*x)/(-9+x^2)
Limit of (-8+x^2+2*x)/(8-x^3)
Sum of series
:
21
Identical expressions
twenty-one
21
twenty minus one
Similar expressions
(1+n+2^(1+n))/(n+2^n)
log(4+3*n)^2*(1+n)/(n*log(1+3*n)^2)
x*cot(3)^2*(1-cos(5*x))
Limit of the function
/
21
Limit of the function 21
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 21 x->0+
lim
x
→
0
+
21
\lim_{x \to 0^+} 21
x
→
0
+
lim
21
Limit(21, x, 0)
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
-1.0
-0.8
-0.6
-0.4
-0.2
1.0
0.0
0.2
0.4
0.6
0.8
21.00
21.01
Plot the graph
Other limits x→0, -oo, +oo, 1
lim
x
→
0
−
21
=
21
\lim_{x \to 0^-} 21 = 21
x
→
0
−
lim
21
=
21
More at x→0 from the left
lim
x
→
0
+
21
=
21
\lim_{x \to 0^+} 21 = 21
x
→
0
+
lim
21
=
21
lim
x
→
∞
21
=
21
\lim_{x \to \infty} 21 = 21
x
→
∞
lim
21
=
21
More at x→oo
lim
x
→
1
−
21
=
21
\lim_{x \to 1^-} 21 = 21
x
→
1
−
lim
21
=
21
More at x→1 from the left
lim
x
→
1
+
21
=
21
\lim_{x \to 1^+} 21 = 21
x
→
1
+
lim
21
=
21
More at x→1 from the right
lim
x
→
−
∞
21
=
21
\lim_{x \to -\infty} 21 = 21
x
→
−
∞
lim
21
=
21
More at x→-oo
Rapid solution
[src]
21
21
21
21
Expand and simplify
One‐sided limits
[src]
lim 21 x->0+
lim
x
→
0
+
21
\lim_{x \to 0^+} 21
x
→
0
+
lim
21
21
21
21
21
= 21
lim 21 x->0-
lim
x
→
0
−
21
\lim_{x \to 0^-} 21
x
→
0
−
lim
21
21
21
21
21
= 21
= 21
Numerical answer
[src]
21
21
The graph