y=|sinπ/2×x|+|cosπ/2×x|的周期

题目

y=|sinπ/2×x|+|cosπ/2×x|的周期

答案

y=|sinπ/2×x|+|cosπ/2×x|的最小正周期为1
f(x+1)=|sinπ/2(x+1)|+|cosπ/2(x+1)
=|sin(π/2x+π/2)|+|cos(π/2x+π/2)|
=|cosπ/2x|+|sinπ/2x|
=f(x)
∴f(x)的最小正周期为1