Question

Find the limit using L'Hopital 's rule
lim x-> infinity x^2 sin(1/x)

is it possible to do it using L'Hopital rule?

Answer 1

rewrite it as \[\huge \frac{ \sin (1/x) }{ 1/x^2 }\] so that L'Hopital's rule can be used.

Answer 2

that's what i did too... it is 0/0.. and then i differetiate it, and it turns out to be a mess o_o

Answer 3

derivative of sin 1/x is -1/x^2 cos (1/x)

Answer 4

umm..shouldnt it be 1/x^-2

Answer 5

-1/x^-2 cos x / (-2x^-3)

Answer 6

then cancel the common factor (-1/x^-2)

Answer 7

then left with cos (1/x) / 2/x

it will become 1/ 0 then

Answer 8

yes, and that is infinity

Answer 9

isnt that undefined..?