cos(1/x) is always bounded between ±1, so whatever value it takes in that range, the product |x|*cos(1/x) will always be in the range -x to x. Hence, in the limit when x is zero so also |x|*cos(1/x) will be zero.
cos(1/x) is always bounded between ±1, so whatever value it takes in that range, the product |x|*cos(1/x) will always be in the range -x to x. Hence, in the limit when x is zero so also |x|*cos(1/x) will be zero.
