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If (cos x)/(sin ax) is periodic function...

If `(cos x)/(sin ax)` is periodic function, then
` lim_(mrarroo)(1+cos^(2m)n!pia)` is equal to

A

0

B

1

C

2

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
C
If `(cosx)/(sin ax)` is periodic then a must be rational.
Now, a is rational and `n rarr oo`. Thus, `n!pia` will become an integral multiple of `pi`.
`therefore" "underset(nrarroo)(lim)(1+cos^(2m)n!pia)=1+(pm1)^(2m)=2`
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  4. The value of lim(xrarr0) (sqrt(1-cosx^(2)))/(1-cos x) is

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  5. lim(xrarr(pi)/(2)) (1-sinx)tanx=

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  6. The value of lim(xrarroo) x^(2)(1-cos.(1)/(x)) is

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  7. lim(xrarroo) root3(x)(root3((x+1)^(2))-root3((x-1)^(2)))=

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  9. undersetlim(Xrarr2^(+)) {x}(sin(x-2))/((x-2)^(2))= (where {.} denotes ...

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  13. The value of lim(xrarr(pi)/(4)) (sqrt(1-sqrt(sin2x)))/(pi-4x) is

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  14. The value of lim(xrarroo) (e^(sqrt(x^(4)+))-e^((x^(2)+1))) is

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  15. The value of lim(xrarrpi//4) (tan^(3)x-tanx)/(cos(x+(pi)/(4))) is

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  20. If k in I such that lim(nrarroo) (cos.(kpi)/(4))^(2n)-(cos.(kpi)/(6))^...

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