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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