Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
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Limit of -1+cos(x)
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Limit of (-1+cos(2*x))/x^2
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Limit of atan(2*x)^(2*sin(x))
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Limit of (-4*x+asin(4*x))/x^3
- Sum of series:
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1/(n*sqrt(log(n)))
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Identical expressions
- one /(n*sqrt(log(n)))
- 1 divide by (n multiply by square root of ( logarithm of (n)))
- one divide by (n multiply by square root of ( logarithm of (n)))
- 1/(n*√(log(n)))
- 1/(nsqrt(log(n)))
- 1/nsqrtlogn
- 1 divide by (n*sqrt(log(n)))
Limit of the function 1/(n*sqrt(log(n)))
The solution
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1
lim ------------
n->oo ________
n*\/ log(n)
$$\lim_{n \to \infty} \frac{1}{n \sqrt{\log{\left(n \right)}}}$$
Limit(1/(n*sqrt(log(n))), n, oo, dir='-')
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
$$\lim_{n \to \infty} \frac{1}{n \sqrt{\log{\left(n \right)}}} = 0$$
$$\lim_{n \to 0^-} \frac{1}{n \sqrt{\log{\left(n \right)}}} = \infty i$$
More at n→0 from the left
$$\lim_{n \to 0^+} \frac{1}{n \sqrt{\log{\left(n \right)}}} = - \infty i$$
More at n→0 from the right
$$\lim_{n \to 1^-} \frac{1}{n \sqrt{\log{\left(n \right)}}} = - \infty i$$
More at n→1 from the left
$$\lim_{n \to 1^+} \frac{1}{n \sqrt{\log{\left(n \right)}}} = \infty$$
More at n→1 from the right
$$\lim_{n \to -\infty} \frac{1}{n \sqrt{\log{\left(n \right)}}} = 0$$
More at n→-oo
$$\lim_{n \to 0^-} \frac{1}{n \sqrt{\log{\left(n \right)}}} = \infty i$$
More at n→0 from the left
$$\lim_{n \to 0^+} \frac{1}{n \sqrt{\log{\left(n \right)}}} = - \infty i$$
More at n→0 from the right
$$\lim_{n \to 1^-} \frac{1}{n \sqrt{\log{\left(n \right)}}} = - \infty i$$
More at n→1 from the left
$$\lim_{n \to 1^+} \frac{1}{n \sqrt{\log{\left(n \right)}}} = \infty$$
More at n→1 from the right
$$\lim_{n \to -\infty} \frac{1}{n \sqrt{\log{\left(n \right)}}} = 0$$
More at n→-oo
The graph