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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: Radon challenger series Part-4
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Radon222 (166)

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\text{If }A_i=\frac{x-a_i}{|x-a_i|},i=1,2,3,.....,n \text{ and if } a_1<a_2<a_3<.....<a_n. \\ \\    \text{Then } \displaystyle\lim_{x\to a_m}(A_1,A_2,A_3,...A_n), 1\le m\le n \text{ is equal to }\\ \\    a) (-1)^m \\ \\   b)(-1)^{m+1}\\ \\  c)(-1)^{m-1}\\ \\  d)\text{does not exist}

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elastiboysai (2332)

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does not exist
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amitp91 (313)

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option d . rate if i  right


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Radon222 (166)

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Too good ! Both of you are correct.

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elastiboysai (2332)

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Explanation:
Right hand limit is +1
Left hand limit is -1
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sboosy (3063)

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answer is D ...as already pointed out by others ..
it can be looked at in another way also ..
it is after all the reciprocal of derivative of |x| as the quantity x tends to zero
differentiation of |x| is |x|/x
instead here we have x/|x|
now we know |x| is not differentiable at x=0
so its derivative's limit shud not exist
which is the question
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