finding limit

[Mr. Ne Ed help]

Hello. I could not figure out this limit problem. please help.

lim (x->positive infinity) xtan(1/x) = ?

I was trying to use L'hospital rule (sorry if I spell it wrong) but I got stuck later on. Thanks.

 

[pka]

xtan(1/x)=[sin(1/x)/(1/x)][1/cos(1/x)].
As x→∞, (1/x)→0.