What is the limit of # ln(ln(x))/x# as x approaches #oo#?

Answer 1

#0#

simply because #x# outgrows #ln x# we know that this is going to be zero, but as it is in #oo/oo# indeterminate form, we can use L'Hopital's rule

#lim_(x to oo) ln(ln(x))/x#

#= lim_(x to oo)( 1/ln(x)* 1/x) /1#

and the limit of the product is the product of the limits #= lim_(x to oo) 1/ln(x)* lim_(x to oo) 1/x = 0#

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Answer 2

Isabella Ackerman

The limit of ln(ln(x))/x as x approaches infinity is 0.

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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.

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