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Limit of the function
:
Limit of (2+x^2-3*x)/(3+x^2-4*x)
Limit of (a+x^2-x*(1+a))/(x^3-a^3)
Limit of (-tan(x)+sin(x))/x^3
Limit of cot(5*x)*tan(3*x)
-12
Identical expressions
- twelve
minus 12
minus twelve
Similar expressions
12
Limit of the function
/
-12
Limit of the function -12
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 (-12) x->4+
lim
x
→
4
+
−
12
\lim_{x \to 4^+} -12
x
→
4
+
lim
−
12
Limit(-12, x, 4)
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
-12.00
-11.99
Plot the graph
One‐sided limits
[src]
lim (-12) x->4+
lim
x
→
4
+
−
12
\lim_{x \to 4^+} -12
x
→
4
+
lim
−
12
-12
−
12
-12
−
12
= -12
lim (-12) x->4-
lim
x
→
4
−
−
12
\lim_{x \to 4^-} -12
x
→
4
−
lim
−
12
-12
−
12
-12
−
12
= -12
= -12
Rapid solution
[src]
-12
−
12
-12
−
12
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim
x
→
4
−
−
12
=
−
12
\lim_{x \to 4^-} -12 = -12
x
→
4
−
lim
−
12
=
−
12
More at x→4 from the left
lim
x
→
4
+
−
12
=
−
12
\lim_{x \to 4^+} -12 = -12
x
→
4
+
lim
−
12
=
−
12
lim
x
→
∞
−
12
=
−
12
\lim_{x \to \infty} -12 = -12
x
→
∞
lim
−
12
=
−
12
More at x→oo
lim
x
→
0
−
−
12
=
−
12
\lim_{x \to 0^-} -12 = -12
x
→
0
−
lim
−
12
=
−
12
More at x→0 from the left
lim
x
→
0
+
−
12
=
−
12
\lim_{x \to 0^+} -12 = -12
x
→
0
+
lim
−
12
=
−
12
More at x→0 from the right
lim
x
→
1
−
−
12
=
−
12
\lim_{x \to 1^-} -12 = -12
x
→
1
−
lim
−
12
=
−
12
More at x→1 from the left
lim
x
→
1
+
−
12
=
−
12
\lim_{x \to 1^+} -12 = -12
x
→
1
+
lim
−
12
=
−
12
More at x→1 from the right
lim
x
→
−
∞
−
12
=
−
12
\lim_{x \to -\infty} -12 = -12
x
→
−
∞
lim
−
12
=
−
12
More at x→-oo
Numerical answer
[src]
-12
-12
The graph