Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of ((-4+3*x)/(2+3*x))^(1+x)/3
-
Limit of (-16+2^x)/(-1+5*sqrt(x)*(5-x))
-
Limit of (-14+x^2-5*x)/(-6+x+2*x^2)
-
Limit of (3+x^2+4*x)/(1+x^3)
- Sum of series:
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2/n
-
Identical expressions
- two /n
- 2 divide by n
- two divide by n
-
Similar expressions
- (3-n+2*n^2)/n^2
- log((1+n^2)/n^2)/log((1+(1+n)^2)/(1+n)^2)
- (1+n+(1+n)^2)/(n+n^2)
Limit of the function 2/n
The solution
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/2\ lim |-| n->oo\n/
$$\lim_{n \to \infty}\left(\frac{2}{n}\right)$$
Limit(2/n, n, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{n \to \infty}\left(\frac{2}{n}\right)$$
Let's divide numerator and denominator by n:
$$\lim_{n \to \infty}\left(\frac{2}{n}\right)$$ =
$$\lim_{n \to \infty}\left(\frac{2 \frac{1}{n}}{1}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{2 \frac{1}{n}}{1}\right) = \lim_{u \to 0^+}\left(2 u\right)$$
=
$$0 \cdot 2 = 0$$
The final answer:
$$\lim_{n \to \infty}\left(\frac{2}{n}\right) = 0$$
$$\lim_{n \to \infty}\left(\frac{2}{n}\right)$$
Let's divide numerator and denominator by n:
$$\lim_{n \to \infty}\left(\frac{2}{n}\right)$$ =
$$\lim_{n \to \infty}\left(\frac{2 \frac{1}{n}}{1}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{2 \frac{1}{n}}{1}\right) = \lim_{u \to 0^+}\left(2 u\right)$$
=
$$0 \cdot 2 = 0$$
The final answer:
$$\lim_{n \to \infty}\left(\frac{2}{n}\right) = 0$$
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
$$\lim_{n \to \infty}\left(\frac{2}{n}\right) = 0$$
$$\lim_{n \to 0^-}\left(\frac{2}{n}\right) = -\infty$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{2}{n}\right) = \infty$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{2}{n}\right) = 2$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{2}{n}\right) = 2$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{2}{n}\right) = 0$$
More at n→-oo
$$\lim_{n \to 0^-}\left(\frac{2}{n}\right) = -\infty$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{2}{n}\right) = \infty$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{2}{n}\right) = 2$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{2}{n}\right) = 2$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{2}{n}\right) = 0$$
More at n→-oo
The graph