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We have f (x) lim(n to oo) cos (x)/(2)...

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

A

0

B

1

C

2

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • 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) sum_(k=1)^(n) tan ((x)/(2^(k))) equals

    A
    `(1)/(x - tan x`
    B
    `(1)/(x) - cot x`
    C
    `x + cot x`
    D
    `x + tan x`

  • 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) sum_(k=1)^(n) (1)/(2^(2k)) sec^(2) ((x)/(2^(k))) equals

    A
    `cosec^(2) x - (1)/(x^(2))`
    B
    `cosec^(2) x + (1)/(x^(2))`
    C
    `cosec^(2) x - x^(2)`
    D
    `cosec^(2) x + x^(2)`

  • The value of: lim_(n to infty) cos(x/2) cos(x/4) cos(x/8)….. Cos(x/2^(n)) is:

    A
    1
    B
    `(sin x)/x`
    C
    `x/(sin x)`
    D
    none of these

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    sin x = 2 ^ (n) * cos (x) / (2) * cos (x) / (2 ^ (2)) * cos (x) / (2 ^ (3)) * ... * cos ( x) / (2 ^ (n)) * sin (x) / (2 ^ (n))

    Let f(x)=lim_(n rarr oo)(sin x)^(2n)

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