求极限(sin(2/n)+cos(3/n))^(-n)

问题描述:

求极限(sin(2/n)+cos(3/n))^(-n)

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)...