Question

f(x) = sin( 1/x ) x -> infinity
is there any horizontal asymptote? if yes find......

Answer 1

well as x->+infinity f(x)->0

Answer 2

so HA would have to be at y=0

Answer 3

but sin(1/x) crosses HA. but f never crosses horizontal asymptote

Answer 4

if the function has a zero then it CAN cross the HA
only vertical asymptotes cannot be crossed

Answer 5

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Answer 6

haha no problem :)