What is #lim_(xrarroo) sin(1/x)/x #?

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What is #lim_(xrarroo) sin(1/x)/x #?

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Answer 1 · 2015-10-30T23:43:37

I found #0#

Explanation:

I would apply the property that says that the limit of a quotient is equal to the quotient of the limits:
#lim_(x->oo)((sin(1/x))/x)=(lim_(x->oo)(sin(1/x)))/(lim_(x->oo)(x))=#
as #x->oo# then #1/x->0# and #sin(1/x)->0# so you get:
#=(lim_(x->oo)(sin(1/x)))/(lim_(x->oo)(x))=0/oo=0#

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What is #lim_(xrarroo) sin(1/x)/x #?

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