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Question

limx01+tanx1+sinxx=


A

1e

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B

1

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C

e

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D

e2

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E

None of these

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Solution

The correct option is B

1


Explanation for the correct option:

Expanding the given equation and applying the limits:

limx01+tanx1+sinx2=limx01+tanx1+sinxx[(1+tanx1+sinx)x=1form]=elimx0x1+tanx1+sinx-1=elimx0x1+tanx-1-sinx1+sinx=elimx0xtanx-sinx1+sinx

Note that this is the determinante form.

Applying the limits,

limx01+tanx1+sinx2=e0tan0+sin01+sin0=e0=1

Thus, limx01+tanx1+sinxx=1

Therefore, the correct answer is option (B).


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