A2. Which of the following statements is correct? The function $f(x)=2+\sin 2x$
(A) never takes the value 2.
(B) is periodic with the smallest period $2\pi$.
(C) reaches its maximum value of 4.
(D) is defined only for $x<\frac{\pi}{4}$.
(E) has no zeros.
A2. Since $f(0)=2$, the function takes the value 2. The smallest period is $\pi$ and the function is defined for all real numbers. Since $\sin 2 x \leq 1$, the maximum value is 3. The correct statement is that the function has no zeros.