The value of ("lim")(xvecoo)(cos"x"/"m")...

The value of `("lim")_(xvecoo)(cos"x"/"m")^("m")` is 1 (b) e (c) `e^(-1)` (d) none of these

A

`underset(xtooo)lim(log_(e)x)/({x})=oo`

B

`underset(xto2^(+))lim(x)/(x^(2)-x-2)=oo`

C

`underset(xto-1^(-))lim(x)/(x^(2)-x-2)=oo`

D

`underset(xtooo)lim(log_(0.5)x)/({x})=oo`

Text Solution

Verified by Experts

The correct Answer is:

A

`underset(mtooo)lim("cos"(x)/(m))^(m)=underset(xtooo)lim[1-(1-"cos"(x)/(m))]^(m)`
`=underset(mtooo)lim[1-2"sin"^(2)(x)/(2m)]^(m)`
`=e^(underset(mtooo)lim(-2"sin"^(2)(x)/(2m))m)=1`

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