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The value of lim(nto oo)cos((x)/(2))cos(...

The value of `lim_(nto oo)cos((x)/(2))cos((x)/(4))cos((x)/(8)). . .((x)/(2^(n)))` is

A

`1`

B

`("sin "x)/(x)`

C

`(x)/("sin "x)`

D

None of these

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The correct Answer is:
B
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We have f (x) lim_(n to oo) cos (x)/(2) cos (x)/(2^(2)) cos (x)/(2^(3)) cos (x)/(2^(4)) …… …. cos (x)/(2^(n)) = ("sin" x)/(2^(n) "sin" (x)/(2^(n))) using the identity lim_(n to oo) lim_(x to 0) f(x) equals