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For some a,b, let f(x)= vmatrixa+ xx&1&b\ &1+ xx&b\ &1&b+ xx vmatrix, x 0, x 0f(x)= + a+ b. Then ( + + )2 is equal to :
(2) 16
As x 0, xx 1, so the limit is the determinant with those entries:
vmatrixa+1&1&b\ &2&b\ &1&b+1 vmatrix R1-R2, R3-R2 vmatrix1&-1&0\ &2&b\\0&-1&1 vmatrix
=1 (2+b)+1 (a)=a+b+2
=2, = =1
( + + )2=42=16
Answer: (2)
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