Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (1+3*x)^(5/x)
-
Limit of x^2/(-2+sqrt(4+x^2))
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Limit of ((5+x^2-6*x)/(5+x^2-5*x))^(2+3*x)
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Limit of (2+x^2+3*x)/(-4+x^2)
- Derivative of:
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x/(9-x^2)
- Integral of d{x}:
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x/(9-x^2)
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Identical expressions
- x/(nine -x^ two)
- x divide by (9 minus x squared )
- x divide by (nine minus x to the power of two)
- x/(9-x2)
- x/9-x2
- x/(9-x²)
- x/(9-x to the power of 2)
- x/9-x^2
- x divide by (9-x^2)
-
Similar expressions
- (3+x)/(9-x^2)
- (3-x)/(9-x^2)
- (-3+sqrt(6+x))/(9-x^2)
- x/(9+x^2)
- (-15+x^2+2*x)/(9-x^2)
- (-1+sqrt(-2+x))/(9-x^2)
Limit of the function x/(9-x^2)
The solution
You have entered
[src]
/ x \
lim |------|
x->-3+| 2|
\9 - x /
$$\lim_{x \to -3^+}\left(\frac{x}{9 - x^{2}}\right)$$
Limit(x/(9 - x^2), x, -3)
Detail solution
Let's take the limit
$$\lim_{x \to -3^+}\left(\frac{x}{9 - x^{2}}\right)$$
transform
$$\lim_{x \to -3^+}\left(\frac{x}{9 - x^{2}}\right)$$
=
$$\lim_{x \to -3^+}\left(\frac{x}{\left(-1\right) \left(x - 3\right) \left(x + 3\right)}\right)$$
=
$$\lim_{x \to -3^+}\left(- \frac{x}{x^{2} - 9}\right) = $$
The final answer:
$$\lim_{x \to -3^+}\left(\frac{x}{9 - x^{2}}\right) = -\infty$$
$$\lim_{x \to -3^+}\left(\frac{x}{9 - x^{2}}\right)$$
transform
$$\lim_{x \to -3^+}\left(\frac{x}{9 - x^{2}}\right)$$
=
$$\lim_{x \to -3^+}\left(\frac{x}{\left(-1\right) \left(x - 3\right) \left(x + 3\right)}\right)$$
=
$$\lim_{x \to -3^+}\left(- \frac{x}{x^{2} - 9}\right) = $$
False
= -oo
The final answer:
$$\lim_{x \to -3^+}\left(\frac{x}{9 - x^{2}}\right) = -\infty$$
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 |------|
x->-3+| 2|
\9 - x /
$$\lim_{x \to -3^+}\left(\frac{x}{9 - x^{2}}\right)$$
-oo
$$-\infty$$
= -75.4165745856354
/ x \
lim |------|
x->-3-| 2|
\9 - x /
$$\lim_{x \to -3^-}\left(\frac{x}{9 - x^{2}}\right)$$
oo
$$\infty$$
= 75.5832414553473
= 75.5832414553473
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to -3^-}\left(\frac{x}{9 - x^{2}}\right) = -\infty$$
More at x→-3 from the left
$$\lim_{x \to -3^+}\left(\frac{x}{9 - x^{2}}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{x}{9 - x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x}{9 - x^{2}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{9 - x^{2}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{9 - x^{2}}\right) = \frac{1}{8}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{9 - x^{2}}\right) = \frac{1}{8}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{9 - x^{2}}\right) = 0$$
More at x→-oo
More at x→-3 from the left
$$\lim_{x \to -3^+}\left(\frac{x}{9 - x^{2}}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{x}{9 - x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x}{9 - x^{2}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{9 - x^{2}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{9 - x^{2}}\right) = \frac{1}{8}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{9 - x^{2}}\right) = \frac{1}{8}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{9 - x^{2}}\right) = 0$$
More at x→-oo
The graph