limx→∞ x4⋅sin⁡1x+x21+|x|3 is equal to

limx→∞ x4⋅sin⁡1x+x21+|x|3=limx→∞ xsin⁡1x+1x1x3+|x|3x3[dividing numerator and denominator by y2]                                   =limx→∞ sin⁡1x1x+limx→∞ 1xlimx→∞ 1x3+limx→∞ |x|3x3=1−00+1=1