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Limit of the function
:
Limit of ((-1+x)/(5+4*x))^(3*x)
Limit of (2+sqrt(x)-sqrt(2))/x
Limit of (x^2+3*x^3)/(x^4-2*x^2+3*x^3)
Limit of ((3+2*x)/(1+x))^x
Identical expressions
((three + two *x)/(one +x))^x
((3 plus 2 multiply by x) divide by (1 plus x)) to the power of x
((three plus two multiply by x) divide by (one plus x)) to the power of x
((3+2*x)/(1+x))x
3+2*x/1+xx
((3+2x)/(1+x))^x
((3+2x)/(1+x))x
3+2x/1+xx
3+2x/1+x^x
((3+2*x) divide by (1+x))^x
Similar expressions
((3+2*x)/(1-x))^x
((3-2*x)/(1+x))^x
Limit of the function
/
((3+2*x)/(1+x))^x
Limit of the function ((3+2*x)/(1+x))^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 /3 + 2*x\ lim |-------| x->oo\ 1 + x /
lim
x
→
∞
(
2
x
+
3
x
+
1
)
x
\lim_{x \to \infty} \left(\frac{2 x + 3}{x + 1}\right)^{x}
x
→
∞
lim
(
x
+
1
2
x
+
3
)
x
Limit(((3 + 2*x)/(1 + x))^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
2000
Plot the graph
Rapid solution
[src]
oo
∞
\infty
∞
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim
x
→
∞
(
2
x
+
3
x
+
1
)
x
=
∞
\lim_{x \to \infty} \left(\frac{2 x + 3}{x + 1}\right)^{x} = \infty
x
→
∞
lim
(
x
+
1
2
x
+
3
)
x
=
∞
lim
x
→
0
−
(
2
x
+
3
x
+
1
)
x
=
1
\lim_{x \to 0^-} \left(\frac{2 x + 3}{x + 1}\right)^{x} = 1
x
→
0
−
lim
(
x
+
1
2
x
+
3
)
x
=
1
More at x→0 from the left
lim
x
→
0
+
(
2
x
+
3
x
+
1
)
x
=
1
\lim_{x \to 0^+} \left(\frac{2 x + 3}{x + 1}\right)^{x} = 1
x
→
0
+
lim
(
x
+
1
2
x
+
3
)
x
=
1
More at x→0 from the right
lim
x
→
1
−
(
2
x
+
3
x
+
1
)
x
=
5
2
\lim_{x \to 1^-} \left(\frac{2 x + 3}{x + 1}\right)^{x} = \frac{5}{2}
x
→
1
−
lim
(
x
+
1
2
x
+
3
)
x
=
2
5
More at x→1 from the left
lim
x
→
1
+
(
2
x
+
3
x
+
1
)
x
=
5
2
\lim_{x \to 1^+} \left(\frac{2 x + 3}{x + 1}\right)^{x} = \frac{5}{2}
x
→
1
+
lim
(
x
+
1
2
x
+
3
)
x
=
2
5
More at x→1 from the right
lim
x
→
−
∞
(
2
x
+
3
x
+
1
)
x
=
0
\lim_{x \to -\infty} \left(\frac{2 x + 3}{x + 1}\right)^{x} = 0
x
→
−
∞
lim
(
x
+
1
2
x
+
3
)
x
=
0
More at x→-oo
The graph