1. if lim x⁹-a⁹/x-a =lim (4+x),find all possible values of a.

x->a x->5

x⁹-a⁹= (x³)³-(a³)³  =(x³-a³)(x⁶+a⁶+(ax)³)

                             =(x-a)(x²+a²+ax)(x⁶+a⁶+(ax)³)

after putting this ,expression becomes

  lim x->a    (x²+a²+ax)(x⁶+a⁶+(ax)³) =  lim x->5  (4+x)

after taking limit

                 (3a²)(3a⁶)=9

                    a⁸=1

 a=-1 or 1 a ns

POSSIBLE VALUE OF A IS +1 OR -1.  BECAUSE FOR FIRST LIMIT THATS GONNA BE 9a⁸ AND FOR SECOND LIMIT ITS GONNA BE 9.  HENCE

9a⁸=9

a=+1 AND -1

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