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Question

For all x(0,1)


A

ex<1+x

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B

loge(1+x)<x

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C

sinx>x

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D

logex>x

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Solution

The correct option is B

loge(1+x)<x


The explanation of the correct option :

Let g(x)=log(1+x)x then

g'(x)=11+x-1=-x1+x<0,x(0,1)

g(x) is decreasing on (0,1).

x>0

We have g(x)<g(0)

loge(1+x)x<0loge(1+x)<x

Hence, the correct option is (B).


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