With the sandwich method :
Because the range of the cosine function is from negative 1 to positive 1, whenever you multiply a number by the sine of anything, the result either stays the same distance from zero or gets closer to zero. Thus, xcos(x) will never get above |x| or below -|x|. So...
When you solve limit problems first of all try substitution, and other methods come after, like the usage of the calculator, sandwich limit and algebra.
In this case begin by substitution :
When you plug 0 into xcos(x) you got 0*cos(0) (remember cosine of 0 equals 1),
we have now 0*1...