Let $$f : \left[-\frac{\pi}{2}, \frac{\pi}{2} \right] \rightarrow R$$ be a continuous function such that
$$f(0)= 1$$ and $$\int_{0}^{\frac{\pi}{3}} f\left(t\right)dt = 0$$
Then which of the following statements is (are) TRUE ?

A

The equation $$f\left(𝑥\right) − 3 \cos 3𝑥 = 0$$ has at least one solution in $$(0,\frac{\pi}{3})$$

B

The equation $$f\left(𝑥\right) − 3 \sin 3𝑥 = −\frac{6}{\pi}$$ has at least one solution in $$(0,\frac{\pi}{3})$$

C

$$lim_{x\rightarrow 0}\frac{x \int_{0}^{x}f\left(t\right)dt}{1-e^{x^{2}}} = -1$$

D

$$lim_{x\rightarrow 0}\frac{\sin x \int_{0}^{x}f\left(t\right)dt}{x^{2}} = -1$$