lim(x→∞) [cos(1/x)+sin(2/x)]^(1/x),=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...