设f(x)={sinπx x<0,f(x-1)+1 (x≥0) }和g(x)={cosxπ (x<1/2),g(x-1)+1 (x≥1/2)}求g(1/4)+f(1/3)+g(5/6)+f(3/4)
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![设f(x)={sinπx x<0,f(x-1)+1 (x≥0) }和g(x)={cosxπ (x<1/2),g(x-1)+1 (x≥1/2)}求g(1/4)+f(1/3)+g(5/6)+f(3/4)](/uploads/image/z/13373790-6-0.jpg?t=%E8%AE%BEf%EF%BC%88x%EF%BC%89%3D%7Bsin%CF%80x+x%EF%BC%9C0%2Cf%EF%BC%88x-1%EF%BC%89%2B1+%EF%BC%88x%E2%89%A50%EF%BC%89+%7D%E5%92%8Cg%EF%BC%88x%EF%BC%89%3D%7Bcosx%CF%80+%EF%BC%88x%EF%BC%9C1%2F2%EF%BC%89%2Cg%EF%BC%88x-1%EF%BC%89%2B1+%EF%BC%88x%E2%89%A51%2F2%EF%BC%89%7D%E6%B1%82g%EF%BC%881%2F4%EF%BC%89%2Bf%EF%BC%881%2F3%EF%BC%89%2Bg%EF%BC%885%2F6%EF%BC%89%2Bf%EF%BC%883%2F4%EF%BC%89)
设f(x)={sinπx x<0,f(x-1)+1 (x≥0) }和g(x)={cosxπ (x<1/2),g(x-1)+1 (x≥1/2)}求g(1/4)+f(1/3)+g(5/6)+f(3/4)
设f(x)={sinπx x<0,f(x-1)+1 (x≥0) }和
g(x)={cosxπ (x<1/2),g(x-1)+1 (x≥1/2)}
求g(1/4)+f(1/3)+g(5/6)+f(3/4)
设f(x)={sinπx x<0,f(x-1)+1 (x≥0) }和g(x)={cosxπ (x<1/2),g(x-1)+1 (x≥1/2)}求g(1/4)+f(1/3)+g(5/6)+f(3/4)
g(1/4)=cos(1/4)π =2分之根号2
f(1/3)=sin(-2/3)π +1=-sin(2/3)π +1=1-2分之根号3
g(5/6)=g(5/6-1)+1=g(-1/6)π +1=g(1/6)π +1=cos(1/6)π +1=1+2分之根号3
f(3/4)=f(-1/3)π +1=sin(-1/3)π +1=-sin(1/3)π +1=1-2分之根号2
所以,g(1/4)+f(1/3)+g(5/6)+f(3/4)=2分之根号2+1-2分之根号3+1+2分之根号3+1-2分之根号2=2
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