How can ı solve this problem without using L'hopital? ln(ln(x)) as x goes +infinity

Answer 1

This limit cannot be found using l'Hopital.

As #x# increases without bound, #lnx# also increases without bound. Therefore #ln(lnx)# increases without bound.
#lim_(xrarroo)ln(lnx) = oo#
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Answer 2

As x approaches positive infinity, the natural logarithm of the natural logarithm of x, ln(ln(x)), also approaches positive infinity.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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