Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (1-log(7*x))^(7*x)
-
Limit of sin(x)/sqrt(1-cos(x))
-
Limit of (e^x-e^2)/(-2+x)
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Limit of tan(3*x)/(7*x)
- Integral of d{x}:
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y^3
- Graphing y =:
- y^3
- Derivative of:
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y^3
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Identical expressions
- y^ three
- y cubed
- y to the power of three
- y3
- y³
- y to the power of 3
-
Similar expressions
- 2*y^4+x*y^3-3*x^2*y^2
- (x+y)^3/(x^2+y^2)
Limit of the function y^3
The solution
Detail solution
Let's take the limit
$$\lim_{y \to \infty} y^{3}$$
Let's divide numerator and denominator by y^3:
$$\lim_{y \to \infty} y^{3}$$ =
$$\lim_{y \to \infty} \frac{1}{\frac{1}{y^{3}}}$$
Do Replacement
$$u = \frac{1}{y}$$
then
$$\lim_{y \to \infty} \frac{1}{\frac{1}{y^{3}}} = \lim_{u \to 0^+} \frac{1}{u^{3}}$$
=
$$\frac{1}{0} = \infty$$
The final answer:
$$\lim_{y \to \infty} y^{3} = \infty$$
$$\lim_{y \to \infty} y^{3}$$
Let's divide numerator and denominator by y^3:
$$\lim_{y \to \infty} y^{3}$$ =
$$\lim_{y \to \infty} \frac{1}{\frac{1}{y^{3}}}$$
Do Replacement
$$u = \frac{1}{y}$$
then
$$\lim_{y \to \infty} \frac{1}{\frac{1}{y^{3}}} = \lim_{u \to 0^+} \frac{1}{u^{3}}$$
=
$$\frac{1}{0} = \infty$$
The final answer:
$$\lim_{y \to \infty} y^{3} = \infty$$
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
Other limits y→0, -oo, +oo, 1
$$\lim_{y \to \infty} y^{3} = \infty$$
$$\lim_{y \to 0^-} y^{3} = 0$$
More at y→0 from the left
$$\lim_{y \to 0^+} y^{3} = 0$$
More at y→0 from the right
$$\lim_{y \to 1^-} y^{3} = 1$$
More at y→1 from the left
$$\lim_{y \to 1^+} y^{3} = 1$$
More at y→1 from the right
$$\lim_{y \to -\infty} y^{3} = -\infty$$
More at y→-oo
$$\lim_{y \to 0^-} y^{3} = 0$$
More at y→0 from the left
$$\lim_{y \to 0^+} y^{3} = 0$$
More at y→0 from the right
$$\lim_{y \to 1^-} y^{3} = 1$$
More at y→1 from the left
$$\lim_{y \to 1^+} y^{3} = 1$$
More at y→1 from the right
$$\lim_{y \to -\infty} y^{3} = -\infty$$
More at y→-oo
The graph