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Question

Evaluate: limx0sinxx


A

1

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B

0

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C

positive infinity

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D

does not exist

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Solution

The correct option is D

does not exist


Explanation for the correct option:

Step-1 Finding the left hand limit:

Consider the given Equation as,

I=limx0sinxx

Find the the LHS, when x0-h[Where,h>0]

I=limh0sin0-h0-hI=limh0sin-h-hI=limh0sinh-hI=-1

Step-2 Finding the right hand limit:

Find the the RHS, when x0+h[Where,h>0]

I=limh0sin0+h0+hI=limh0sinhhI=limh0sinhhI=1

Since, LHLRHL

Hence, The limit does not exist.

Therefore, the correct answer is option D.


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