Lim_x→-∞ x⁴ sin(1/x) + x² / 1 + ¦x¦³ ←( mod x )³ equals :

Hi

I will take the question as

lim_x→-∞  x⁴ sin1/x + x²

            ______________

              1+ (mod x)³

as _x→-∞  so mod x = - x

put y = 1/x

lim _y->0 siny/y⁴ + 1/y²

            ----------------

             1 - 1/y³

Multiply num and denom by y³

lim_{y-> 0} (siny/y - y)/(y³-1) = -1

Thanks

Anurag Kishore