Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((-2+3*x)/(1+3*x))^(2*x)
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Limit of (x/(1+2*x))^x
- Limit of n2*(5/2+n/2)
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Limit of (1-cos(4*x))/(1-cos(8*x))
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Identical expressions
- log(log(x))/x
- logarithm of ( logarithm of (x)) divide by x
- loglogx/x
- log(log(x)) divide by x
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Similar expressions
- (1+x)*log(log(x))/(x*log(log(1+x)))
- log(log(x))/(x-e)
Limit of the function log(log(x))/x
The solution
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/log(log(x))\ lim |-----------| x->oo\ x /
$$\lim_{x \to \infty}\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{x}\right)$$
Limit(log(log(x))/x, x, oo, dir='-')
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{x}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{x}\right) = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{x}\right) = -\infty$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{x}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{x}\right) = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{x}\right) = -\infty$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{x}\right) = 0$$
More at x→-oo
The graph