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If lim(x to 0) (cos x + a^(3)sin(b^(6)x)...

If `lim_(x to 0) (cos x + a^(3)sin(b^(6)x))^(1//x)=e^(512)`, then the value of `ab^(2)` is equal to

A

`-512`

B

512

C

8

D

`16sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`= e^(lim_(x to 0)(cos x + a^(3)sin(b^(6)x)-1)x(1)/(x))`
`= e^(lim_(x to 0)-(sin x+a^(3)cos(b^(6)x).b^(6))/(1))`
`= e^(a^(3)b^(6))`
`therefore a^(3)b^(6)=512 rArr ab^(2)=8`
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