1. if lim x³-a^3/x-a =lim x⁴-1/x-1 ,find all possible values of a.

x->a x->1

lim x->a  (x³-a³)/x-a =  lim x->1  x⁴-1/x-1                

x³-a³=(x-a)(x²+a²+ax)       &     x⁴-1=(x²-1)(x²+1)=(x-1)(x+1)(x²+1)

putting these expression becomes

lim x->a   (x²+a²+ax)      =    lim x->1 (x+1)(x²+1)

      after  taking limit

          3a² = 4

           a=(4/3)^1/2

a=2/3^1/2 or -2/3^1/2