\infty} {(cos \frac{4}{x})}^x=lim_{x->\infty} (1-2sin^2 \frac{2}{x})^x=\\\\ lim_{t->0} (1-2sin^2 t)^{\frac{t}{2}}=|1^0|=1" alt="lim_{x->\infty} {(cos \frac{4}{x})}^x=lim_{x->\infty} (1-2sin^2 \frac{2}{x})^x=\\\\ lim_{t->0} (1-2sin^2 t)^{\frac{t}{2}}=|1^0|=1" align="absmiddle" class="latex-formula">