1.1. Find the maximum value of the function $\sin ^{13} x+\cos ^{14} x$.
1.1. Answer: 1. Note that $\sin ^{13} x+\cos ^{14} x \leqslant \sin ^{2} x+\cos ^{2} x=1$, and, for example, at $x=\pi / 2$ equality is achieved.