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If f(x)=lim(m->oo) lim(n->oo)cos^(2m) n!...

If `f(x)=lim_(m->oo) lim_(n->oo)cos^(2m) n!pix` then the range of f(x) is

A

`f(sqrt(3))=1`

B

`f(3)=1`

C

`f(sqrt(2))=0`

D

`f(1)=2`

Text Solution

Verified by Experts

The correct Answer is:
B, C
When `x=` rational then `cosn!pix=+-1`
so `f(x)=1`
When `x=` irrational then `cosn!pixepsilon(-1,0)uu(0,1)`
`impliesf(x)=0`
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