1. if lim x 3 -a 3/ x-a =lim x 4 -1/x-1 ,find all possible values of a. x->a x->1

1.   if lim x3-a3/x-a =lim x4-1/x-1 ,find all possible values of a.

       x->a                  x->1

Grade:Upto college level

1 Answers

vikas askiitian expert
509 Points
13 years ago

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=2/31/2 or -2/31/2

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