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1. if lim x3-a3/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=2/31/2 or -2/31/2
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