If x 0 ax2ex-b e(1+x)+cxe-xx2 x=1, then 16 (a2+b2+c2 ) is equal to .
81
Denominator x2 x x3; expand the numerator up to x3:
ax2(1+x)-b (x- x22+ x33 )+cx (1-x+ x22 )
=(c-b)x+ (a+ b2-c )x2+ (a- b3+ c2 )x3+
Limit = 1 c-b=0, a+ b2-c=0, a- b3+ c2=1
c=b, a= b2, 2b3=1 b=c= 32, a= 34
16 ( 916+ 94+ 94 )=9+36+36=81
Answer: 81
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