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