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Question

limx0(1+a3)+8e1/x1+(1b3)e1/x=2 then

A
a=1,b=(3)1/3
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B
a=1,b=31/3
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C
a=1,b=(3)1/3
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D
a=1,b=0
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Solution

The correct option is A a=1,b=(3)1/3
We have,
limx0(1+a3)+8e1/x1+(1b3)e1/x=2
[form]
limx0(1+a3)e1/x+8e1/x+(1b3)=2
0+80+(1b3)=21b3=4b3=3b=(3)1/3
Again,
limx0(1+a3)+8e1/x1+(1b3)e1/x=2
limx0(1+a3)+8e1/x1+4e1/x=2
1+a3=2 [On comparison]
a=1
Therefore, a=1,b=(3)1/3
Hence, option 'A' is correct.

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