题目

求极限(sin(2/n)+cos(3/n))^(-n)

提问时间：2021-01-01

答案

lim（n→∞）[(sin(2/n)+cos(3/n))^(-n)]=lim（n→∞）[(sin(2/n)+1)^(-n)]=e^[lim（n→∞）(-n)ln(sin(2/n)+1)](等价无穷小替换)=e^[lim（n→∞）(-n)(sin(2/n)]=e^{lim（n→∞）(-2)[(sin(2/n))/(2/n)]}=e^(-2)...