Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-4-7*x+2*x^2)/(4-13*x+3*x^2)
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Limit of sin(7*x)/sin(3*x)
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Limit of (1-cos(x))/(x-sin(x))
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Limit of (7+2*x)^(4/(3+x))
- Sum of series:
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n^3
- Graphing y =:
- n^3
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Identical expressions
- n^ three
- n cubed
- n to the power of three
- n3
- n³
- n to the power of 3
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Similar expressions
- (-1+n^3)/(1+n^2)
- x^x/factorial(n)^3
- (4+3*n^2)/(1+n^2+n^3)
- e^(-n)*n^3
- (1+n^2-3*n)/(n+n^3)
Limit of the function n^3
The solution
Detail solution
Let's take the limit
$$\lim_{n \to \infty} n^{3}$$
Let's divide numerator and denominator by n^3:
$$\lim_{n \to \infty} n^{3}$$ =
$$\lim_{n \to \infty} \frac{1}{\frac{1}{n^{3}}}$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty} \frac{1}{\frac{1}{n^{3}}} = \lim_{u \to 0^+} \frac{1}{u^{3}}$$
=
$$\frac{1}{0} = \infty$$
The final answer:
$$\lim_{n \to \infty} n^{3} = \infty$$
$$\lim_{n \to \infty} n^{3}$$
Let's divide numerator and denominator by n^3:
$$\lim_{n \to \infty} n^{3}$$ =
$$\lim_{n \to \infty} \frac{1}{\frac{1}{n^{3}}}$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty} \frac{1}{\frac{1}{n^{3}}} = \lim_{u \to 0^+} \frac{1}{u^{3}}$$
=
$$\frac{1}{0} = \infty$$
The final answer:
$$\lim_{n \to \infty} n^{3} = \infty$$
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 n→0, -oo, +oo, 1
$$\lim_{n \to \infty} n^{3} = \infty$$
$$\lim_{n \to 0^-} n^{3} = 0$$
More at n→0 from the left
$$\lim_{n \to 0^+} n^{3} = 0$$
More at n→0 from the right
$$\lim_{n \to 1^-} n^{3} = 1$$
More at n→1 from the left
$$\lim_{n \to 1^+} n^{3} = 1$$
More at n→1 from the right
$$\lim_{n \to -\infty} n^{3} = -\infty$$
More at n→-oo
$$\lim_{n \to 0^-} n^{3} = 0$$
More at n→0 from the left
$$\lim_{n \to 0^+} n^{3} = 0$$
More at n→0 from the right
$$\lim_{n \to 1^-} n^{3} = 1$$
More at n→1 from the left
$$\lim_{n \to 1^+} n^{3} = 1$$
More at n→1 from the right
$$\lim_{n \to -\infty} n^{3} = -\infty$$
More at n→-oo
The graph