lim(x→∞) [cos(1/x)+sin(2/x)]^(1/x),这样真的好难打,还不如发图=lim(x→∞) [cos(1/x)+2sin(1/x)cos(1/x)]^(1/x)=lim(x→∞) {cos(1/x)[1+2sin(1/x)cos(1/x)]}^(1/x)=lim(x→∞) [cos(1/x)]^(1/x)*lim(x→∞) [1+2sin(1/x)]^(1/x)=1*lim(x→∞) [1+2sin(1/x)]^{1/[2sin(1/x)]}*[2sin(1/x)]/x=e^2lim(x→∞) sin(1/x)/x=e^0=1
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