Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (2+n)/n
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Limit of exp(1/x)
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Limit of 1-cos(x)/x^2
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Limit of log(2*x)*log(-1+2*x)
- Sum of series:
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n^2
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Identical expressions
- n^ two
- n squared
- n to the power of two
- n2
- n²
- n to the power of 2
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Similar expressions
- n^2/factorial(n)
- exp((1+n)^2)*exp(-n^2)
- (7+n)^2/((6+n)*(8+n))
- cos(n)/n^2
Limit of the function n^2
The solution
Detail solution
Let's take the limit
$$\lim_{n \to \infty} n^{2}$$
Let's divide numerator and denominator by n^2:
$$\lim_{n \to \infty} n^{2}$$ =
$$\lim_{n \to \infty} \frac{1}{\frac{1}{n^{2}}}$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty} \frac{1}{\frac{1}{n^{2}}} = \lim_{u \to 0^+} \frac{1}{u^{2}}$$
=
$$\frac{1}{0} = \infty$$
The final answer:
$$\lim_{n \to \infty} n^{2} = \infty$$
$$\lim_{n \to \infty} n^{2}$$
Let's divide numerator and denominator by n^2:
$$\lim_{n \to \infty} n^{2}$$ =
$$\lim_{n \to \infty} \frac{1}{\frac{1}{n^{2}}}$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty} \frac{1}{\frac{1}{n^{2}}} = \lim_{u \to 0^+} \frac{1}{u^{2}}$$
=
$$\frac{1}{0} = \infty$$
The final answer:
$$\lim_{n \to \infty} n^{2} = \infty$$
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
$$\lim_{n \to \infty} n^{2} = \infty$$
$$\lim_{n \to 0^-} n^{2} = 0$$
More at n→0 from the left
$$\lim_{n \to 0^+} n^{2} = 0$$
More at n→0 from the right
$$\lim_{n \to 1^-} n^{2} = 1$$
More at n→1 from the left
$$\lim_{n \to 1^+} n^{2} = 1$$
More at n→1 from the right
$$\lim_{n \to -\infty} n^{2} = \infty$$
More at n→-oo
$$\lim_{n \to 0^-} n^{2} = 0$$
More at n→0 from the left
$$\lim_{n \to 0^+} n^{2} = 0$$
More at n→0 from the right
$$\lim_{n \to 1^-} n^{2} = 1$$
More at n→1 from the left
$$\lim_{n \to 1^+} n^{2} = 1$$
More at n→1 from the right
$$\lim_{n \to -\infty} n^{2} = \infty$$
More at n→-oo
The graph