limits

Anrwer is 0.

As lim (x→0), sin x≈x and tan x≈x.

.: it becomes lim (x→0) x log x
Above form is 0 X ∞, convert it into ∞/∞ and use L' HOSPITAL RULE. You will get the answer.

i think limit does not exist
since for x→0^- sinx will be negative and the logarithm wont be defined

@aditya
well in that case we must concentrate only on RHL.