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Discussion Response Post to: limits

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Bipin Dubey (13679)

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First one is simple
its x*(an oscillating function)
so as x->0 limit tends to zero.

Second one (i think none of the answers were correct)
limit is [sqrt(1-cos2x)]/x as x -> 0
since sqrt is a +ve function
hence sqrt(1-cos2x) = |sqrt(2)*sin(x)| modulus of sqrt(2)*sin(x)

so limit is L = |sqrt(2)*sin(x)|/x
as x -> minus zero
LHL = -[sqrt(2)*sin(x)] /x = -sqrt(2)

as x -> plus zero
RHL = [sqrt(2)*sin(x)] /x = sqrt(2)

since LHL is not equal to RHL.
therefore the limit not exists.

Bipin Kumar Dubey Chemical Dept. IIT Kharagpur

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