Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-5+7*n)/(2+n)
-
Limit of (-64+4^x)/(-3+x)
-
Limit of (-7+3*x^2+5*x)/(1+x+3*x^2)
-
Limit of (-2+2*x^3+7*x)/(-4-x+3*x^3)
- Graphing y =:
- x/(3-x^2)
- Integral of d{x}:
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x/(3-x^2)
-
Identical expressions
- x/(three -x^ two)
- x divide by (3 minus x squared )
- x divide by (three minus x to the power of two)
- x/(3-x2)
- x/3-x2
- x/(3-x²)
- x/(3-x to the power of 2)
- x/3-x^2
- x divide by (3-x^2)
-
Similar expressions
- x/(3+x^2)
Limit of the function x/(3-x^2)
The solution
You have entered
[src]
/ x \
lim |------|
___ | 2|
x->-\/ 3 +\3 - x /
$$\lim_{x \to - \sqrt{3}^+}\left(\frac{x}{3 - x^{2}}\right)$$
Limit(x/(3 - x^2), x, -sqrt(3))
Detail solution
Let's take the limit
$$\lim_{x \to - \sqrt{3}^+}\left(\frac{x}{3 - x^{2}}\right)$$
transform
$$\lim_{x \to - \sqrt{3}^+}\left(\frac{x}{3 - x^{2}}\right)$$
=
$$\lim_{x \to - \sqrt{3}^+}\left(\frac{x}{3 - x^{2}}\right)$$
=
$$\lim_{x \to - \sqrt{3}^+}\left(- \frac{x}{x^{2} - 3}\right) = $$
The final answer:
$$\lim_{x \to - \sqrt{3}^+}\left(\frac{x}{3 - x^{2}}\right) = -\infty$$
$$\lim_{x \to - \sqrt{3}^+}\left(\frac{x}{3 - x^{2}}\right)$$
transform
$$\lim_{x \to - \sqrt{3}^+}\left(\frac{x}{3 - x^{2}}\right)$$
=
$$\lim_{x \to - \sqrt{3}^+}\left(\frac{x}{3 - x^{2}}\right)$$
=
$$\lim_{x \to - \sqrt{3}^+}\left(- \frac{x}{x^{2} - 3}\right) = $$
False
= -oo
The final answer:
$$\lim_{x \to - \sqrt{3}^+}\left(\frac{x}{3 - x^{2}}\right) = -\infty$$
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
One‐sided limits
[src]
/ x \
lim |------|
___ | 2|
x->-\/ 3 +\3 - x /
$$\lim_{x \to - \sqrt{3}^+}\left(\frac{x}{3 - x^{2}}\right)$$
-oo
$$-\infty$$
= -75.3553859659747195948934569606616671399941301276418535221745538834465135920
/ x \
lim |------|
___ | 2|
x->-\/ 3 -\3 - x /
$$\lim_{x \to - \sqrt{3}^-}\left(\frac{x}{3 - x^{2}}\right)$$
oo
$$\infty$$
= 75.6440621556285785180890305930589004538213649891932274519538314706869414410
= 75.6440621556285785180890305930589004538213649891932274519538314706869414410
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to - \sqrt{3}^-}\left(\frac{x}{3 - x^{2}}\right) = -\infty$$
More at x→-sqrt(3) from the left
$$\lim_{x \to - \sqrt{3}^+}\left(\frac{x}{3 - x^{2}}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{x}{3 - x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x}{3 - x^{2}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{3 - x^{2}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{3 - x^{2}}\right) = \frac{1}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{3 - x^{2}}\right) = \frac{1}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{3 - x^{2}}\right) = 0$$
More at x→-oo
More at x→-sqrt(3) from the left
$$\lim_{x \to - \sqrt{3}^+}\left(\frac{x}{3 - x^{2}}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{x}{3 - x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x}{3 - x^{2}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{3 - x^{2}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{3 - x^{2}}\right) = \frac{1}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{3 - x^{2}}\right) = \frac{1}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{3 - x^{2}}\right) = 0$$
More at x→-oo
Numerical answer
[src]
-75.3553859659747195948934569606616671399941301276418535221745538834465135920
-75.3553859659747195948934569606616671399941301276418535221745538834465135920
The graph