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

Answer 1

I found #0#

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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Answer 2

Cameron Alexander

The limit of sin(1/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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