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Question

If limx[1+x+f(x)x]1x=e3 then the value of the function f(x) may be

A
x22
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B
x2
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C
2x2
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D
3x2
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Solution

The correct option is C 2x2
limx[1+x+f(x)x]1x=e3
or limxelimx1+x+f(x)x11x=e3
or limxelimx1+f(x)x2=e3
or limxf(x)x2=2
Then f(x)=2x2

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