Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-9+x^2)/(-3+x^2-2*x)
-
Limit of log(2*x)*log(-1+2*x)
-
Limit of sin(5*x)/(7*pi*x)
-
Limit of 1+x^2
- Sum of series:
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1/n
- Graphing y =:
- 1/n
-
Identical expressions
- one /n
- 1 divide by n
- one divide by n
-
Similar expressions
- 1/(n*log(n))
Limit of the function 1/n
The solution
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1 lim - n->oon
$$\lim_{n \to \infty} \frac{1}{n}$$
Limit(1/n, n, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{n \to \infty} \frac{1}{n}$$
Let's divide numerator and denominator by n:
$$\lim_{n \to \infty} \frac{1}{n}$$ =
$$\lim_{n \to \infty}\left(\frac{1}{n}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{1}{n}\right) = \lim_{u \to 0^+} u$$
=
$$0 = 0$$
The final answer:
$$\lim_{n \to \infty} \frac{1}{n} = 0$$
$$\lim_{n \to \infty} \frac{1}{n}$$
Let's divide numerator and denominator by n:
$$\lim_{n \to \infty} \frac{1}{n}$$ =
$$\lim_{n \to \infty}\left(\frac{1}{n}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{1}{n}\right) = \lim_{u \to 0^+} u$$
=
$$0 = 0$$
The final answer:
$$\lim_{n \to \infty} \frac{1}{n} = 0$$
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
$$\lim_{n \to \infty} \frac{1}{n} = 0$$
$$\lim_{n \to 0^-} \frac{1}{n} = -\infty$$
More at n→0 from the left
$$\lim_{n \to 0^+} \frac{1}{n} = \infty$$
More at n→0 from the right
$$\lim_{n \to 1^-} \frac{1}{n} = 1$$
More at n→1 from the left
$$\lim_{n \to 1^+} \frac{1}{n} = 1$$
More at n→1 from the right
$$\lim_{n \to -\infty} \frac{1}{n} = 0$$
More at n→-oo
$$\lim_{n \to 0^-} \frac{1}{n} = -\infty$$
More at n→0 from the left
$$\lim_{n \to 0^+} \frac{1}{n} = \infty$$
More at n→0 from the right
$$\lim_{n \to 1^-} \frac{1}{n} = 1$$
More at n→1 from the left
$$\lim_{n \to 1^+} \frac{1}{n} = 1$$
More at n→1 from the right
$$\lim_{n \to -\infty} \frac{1}{n} = 0$$
More at n→-oo
The graph