Let \( f(x)=\lim _{n \rightarrow \infty} \frac{3^{n} \sin x+(\sqrt{2} \cos x+2)^{n}+2^{n} \cos x}{3^{n}+\cos x(\sqrt{2} \cos x+2)^{n}} \). Then \( \lim _{x \rightarrow \frac{\pi}{4}^{-}} f(x)=\frac{1}{\sqrt{2}} \) \( \lim _{x \rightarrow \frac{\pi}{4}^{-}} f(x)=\sqrt{2} \) \( \lim _{x \rightarrow \frac{\pi}{4}^{+}} f(x)=\frac{1}{\sqrt{2}} \) \( \lim _{x \rightarrow \frac{\pi^{+}}{4}} f(x)=\sqrt{2} \)
