Mister Exam
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How to use it?
- Limit of the function:
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Limit of log(log(x))
- Limit of sin(factorial(x))
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Limit of sqrt(x)*log(x)
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Limit of sin(sqrt(x))/sqrt(x)
- Derivative of:
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log(log(x))
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Identical expressions
- log(log(x))
- logarithm of ( logarithm of (x))
- loglogx
Limit of the function log(log(x))
The solution
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lim log(log(x)) x->-oo
$$\lim_{x \to -\infty} \log{\left(\log{\left(x \right)} \right)}$$
Limit(log(log(x)), x, -oo)
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
$$\lim_{x \to -\infty} \log{\left(\log{\left(x \right)} \right)} = \infty$$
$$\lim_{x \to \infty} \log{\left(\log{\left(x \right)} \right)} = \infty$$
More at x→oo
$$\lim_{x \to 0^-} \log{\left(\log{\left(x \right)} \right)} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\log{\left(x \right)} \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(\log{\left(x \right)} \right)} = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\log{\left(x \right)} \right)} = -\infty$$
More at x→1 from the right
$$\lim_{x \to \infty} \log{\left(\log{\left(x \right)} \right)} = \infty$$
More at x→oo
$$\lim_{x \to 0^-} \log{\left(\log{\left(x \right)} \right)} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\log{\left(x \right)} \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(\log{\left(x \right)} \right)} = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\log{\left(x \right)} \right)} = -\infty$$
More at x→1 from the right
The graph