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Question

The largest value of the non-negative integer a for which limx1{ax+sin(x1)+ax+sin(x1)1}1x1x=14 is

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Solution

limx1{ax+sin(x1)+ax+sin(x1)1}1x1x
limx1{a(1x)+sin(x1)(x1)+sin(x1)}1+x
limx1⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪a+sin(x1)x11+sin(x1)x1⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪(1+x)
{a+12}2=14
a+12=±12
a+1=±1 a=0,a=2
But at a=2, base becomes negative
a=0

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