lim(x to 0) (sin x + cos 3x)^(2//x) =...

`lim_(x to 0) (sin x + cos 3x)^(2//x)` =

A

1

B

`e^2`

C

`e^(2//3)`

D

does not exist

Verified by Experts

The correct Answer is:

B

`lim_(x to 0) (sin x + cos 3x)^(2/x) = e^(lim_(x to 0) 2/x(sin x + cos 3x - 1)) = e^(2lim_(x to 0) ((sin x)/x + (cos 3x - 1)/1))=e^2`.

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