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Question

If Ai=xai|xai| where i=1,2,3 and a1<a2<a3 then limxa2A1A2A3=

A
1
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B
1
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C
0
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D
does not exist
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Solution

The correct option is C does not exist
The question asks us about,
lim xa2xa1|xa1|×xa2|xa2|×xa3|xa3|
Now, since
lim xa2xa2|xa2| does not exist because
lim xa2xa2|xa2|=1
lim xa2+xa2|xa2|=1
Since, LHL is not equal to RHL , hence the limit does not exist.
Therefore, the limit of the entire function does not exist

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