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Question

If limxax9a9xa=9, find all possible values of a.

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Solution

limxax9a9xa=9...(i)

LHS=limxax9a9xa

=9(a)91

=9a8

It is given that 9a8=9 [from (i)]

a8=99=1

a4=1

a2=1

a=±1

a=1 and a =-1


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