Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of ((2+x)/(4+x))^cos(x)
-
Limit of -5-2*x^2+8*x
-
Limit of (-9+x^2)/(-27+x^3)
-
Limit of 1+7*x+11*x^2/2
- Sum of series:
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2/n^2
-
Identical expressions
- two /n^ two
- 2 divide by n squared
- two divide by n to the power of two
- 2/n2
- 2/n²
- 2/n to the power of 2
- 2 divide by n^2
-
Similar expressions
- cos(n)^2/n^2
- x^5*tan(2/n^2)^3
- (1+n)^2/n^2
- 5-3/n+2/n^2
Limit of the function 2/n^2
The solution
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/2 \
lim |--|
n->oo| 2|
\n /
$$\lim_{n \to \infty}\left(\frac{2}{n^{2}}\right)$$
Limit(2/n^2, n, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{n \to \infty}\left(\frac{2}{n^{2}}\right)$$
Let's divide numerator and denominator by n^2:
$$\lim_{n \to \infty}\left(\frac{2}{n^{2}}\right)$$ =
$$\lim_{n \to \infty}\left(\frac{2 \frac{1}{n^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{2 \frac{1}{n^{2}}}{1}\right) = \lim_{u \to 0^+}\left(2 u^{2}\right)$$
=
$$2 \cdot 0^{2} = 0$$
The final answer:
$$\lim_{n \to \infty}\left(\frac{2}{n^{2}}\right) = 0$$
$$\lim_{n \to \infty}\left(\frac{2}{n^{2}}\right)$$
Let's divide numerator and denominator by n^2:
$$\lim_{n \to \infty}\left(\frac{2}{n^{2}}\right)$$ =
$$\lim_{n \to \infty}\left(\frac{2 \frac{1}{n^{2}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{2 \frac{1}{n^{2}}}{1}\right) = \lim_{u \to 0^+}\left(2 u^{2}\right)$$
=
$$2 \cdot 0^{2} = 0$$
The final answer:
$$\lim_{n \to \infty}\left(\frac{2}{n^{2}}\right) = 0$$
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 n→0, -oo, +oo, 1
$$\lim_{n \to \infty}\left(\frac{2}{n^{2}}\right) = 0$$
$$\lim_{n \to 0^-}\left(\frac{2}{n^{2}}\right) = \infty$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{2}{n^{2}}\right) = \infty$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{2}{n^{2}}\right) = 2$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{2}{n^{2}}\right) = 2$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{2}{n^{2}}\right) = 0$$
More at n→-oo
$$\lim_{n \to 0^-}\left(\frac{2}{n^{2}}\right) = \infty$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{2}{n^{2}}\right) = \infty$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{2}{n^{2}}\right) = 2$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{2}{n^{2}}\right) = 2$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{2}{n^{2}}\right) = 0$$
More at n→-oo
The graph