Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-6+x^2-x)/(6+x^2-5*x)
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Limit of log(1+x^2)/(-e^(-x)+cos(3*x))
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Limit of -2+|-2+x|/x
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Limit of (-4-8*x+8*x^2)/(3+8*x)
- Graphing y =:
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log(log(log(x)))
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Identical expressions
- log(log(log(x)))
- logarithm of ( logarithm of ( logarithm of (x)))
- logloglogx
Limit of the function log(log(log(x)))
The solution
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lim log(log(log(x))) x->oo
$$\lim_{x \to \infty} \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)}$$
Limit(log(log(log(x))), x, 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 x→0, -oo, +oo, 1
$$\lim_{x \to \infty} \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} = \infty$$
$$\lim_{x \to 0^-} \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} = \infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} = \infty$$
More at x→-oo
$$\lim_{x \to 0^-} \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} = \infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(\log{\left(\log{\left(x \right)} \right)} \right)} = \infty$$
More at x→-oo
The graph