Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of x^2*(1/3-cos(8*x)/3)
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Limit of (e^(4*x)-e^(3*x))/(-sin(3*x)+sin(4*x))
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Limit of (e^(5*x)-e^x)/(x^3+asin(x))
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Limit of (9-x)/(-3+x^3)
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Identical expressions
- (nine -x)/(- three +x^ three)
- (9 minus x) divide by ( minus 3 plus x cubed )
- (nine minus x) divide by ( minus three plus x to the power of three)
- (9-x)/(-3+x3)
- 9-x/-3+x3
- (9-x)/(-3+x³)
- (9-x)/(-3+x to the power of 3)
- 9-x/-3+x^3
- (9-x) divide by (-3+x^3)
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Similar expressions
- (9-x)/(3+x^3)
- (9-x)/(-3-x^3)
- (9+x)/(-3+x^3)
Limit of the function (9-x)/(-3+x^3)
The solution
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[src]
/ 9 - x \
lim |-------|
x->0+| 3|
\-3 + x /
$$\lim_{x \to 0^+}\left(\frac{9 - x}{x^{3} - 3}\right)$$
Limit((9 - x)/(-3 + x^3), 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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{9 - x}{x^{3} - 3}\right) = -3$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{9 - x}{x^{3} - 3}\right) = -3$$
$$\lim_{x \to \infty}\left(\frac{9 - x}{x^{3} - 3}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{9 - x}{x^{3} - 3}\right) = -4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{9 - x}{x^{3} - 3}\right) = -4$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{9 - x}{x^{3} - 3}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{9 - x}{x^{3} - 3}\right) = -3$$
$$\lim_{x \to \infty}\left(\frac{9 - x}{x^{3} - 3}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{9 - x}{x^{3} - 3}\right) = -4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{9 - x}{x^{3} - 3}\right) = -4$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{9 - x}{x^{3} - 3}\right) = 0$$
More at x→-oo
One‐sided limits
[src]
/ 9 - x \
lim |-------|
x->0+| 3|
\-3 + x /
$$\lim_{x \to 0^+}\left(\frac{9 - x}{x^{3} - 3}\right)$$
-3
$$-3$$
= -3.0
/ 9 - x \
lim |-------|
x->0-| 3|
\-3 + x /
$$\lim_{x \to 0^-}\left(\frac{9 - x}{x^{3} - 3}\right)$$
-3
$$-3$$
= -3.0
= -3.0
The graph