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Question

If limx1(tan(x+1)+a(e.ex+x)xa2sin1(x+1)+1)x+1x+21=1,
then possible values of a is/are

A
2
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B
0
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C
3+1
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D
31
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Solution

The correct option is C 3+1
limx1(tan(x+1)+aex+1+ax+aax+1a2sin1(x+1))(x+1)(x+2+1)x+1=1
limx1(tan(x+1)+a(ex+11)+a(x+1)x+1a2sin1(x+1))x+2+1=1
limx1⎜ ⎜ ⎜ ⎜tan(x+1)x+1+a(ex+11)x+1+a1a2sin1(x+1)x+1⎟ ⎟ ⎟ ⎟x+2+1=1
(1+a+a1a2)2=1
(1+2a1a2)=±1

a2+2a=0 or a22a2=0
a=0,2 or a=1±3


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