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Let f:[-pi/2,pi/2] to R be a continuous ...

Let `f:[-pi/2,pi/2] to R` be a continuous function such that `f(0)=1 and int_0^(pi/3)f(t)dt=0`
Then which of the following statement is(are) TRUE?

A

The equation `f(x)-3cos3x=0` has at least one solution in `(0,pi/3)`

B

The equation `f(x)-3cos3x=-6/pi` has at least one solution in `(0,pi/3)`

C

`lim_(x to 0)x (int_0^xf(t)dt)/(1-e^(x^2))=-1`

D

`lim_(x to 0) (sinx (int_0^xf(t)dt))/(x^2)=-1`

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