已知f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|≤π/2)是定义域为R的奇函数,且当x=2时,f(x)取得最大值2,则则f(1)+f(2)+f(3)+…+f(100)=答案是2+或2 - 2根号2
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![已知f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|≤π/2)是定义域为R的奇函数,且当x=2时,f(x)取得最大值2,则则f(1)+f(2)+f(3)+…+f(100)=答案是2+或2 - 2根号2](/uploads/image/z/10006402-58-2.jpg?t=%E5%B7%B2%E7%9F%A5f%28x%29%EF%BC%9DAsin%28%CF%89x%EF%BC%8B%CF%86%29%28A%3E0%2C%CF%89%3E0%2C%7C%CF%86%7C%E2%89%A4%CF%80%2F2%29%E6%98%AF%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BAR%E7%9A%84%E5%A5%87%E5%87%BD%E6%95%B0%2C%E4%B8%94%E5%BD%93x%EF%BC%9D2%E6%97%B6%2Cf%28x%29%E5%8F%96%E5%BE%97%E6%9C%80%E5%A4%A7%E5%80%BC2%2C%E5%88%99%E5%88%99f%281%29%EF%BC%8Bf%282%29%EF%BC%8Bf%283%29%EF%BC%8B%E2%80%A6%EF%BC%8Bf%28100%29%EF%BC%9D%E7%AD%94%E6%A1%88%E6%98%AF2%2B%E6%88%962++-+++2%E6%A0%B9%E5%8F%B72)
已知f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|≤π/2)是定义域为R的奇函数,且当x=2时,f(x)取得最大值2,则则f(1)+f(2)+f(3)+…+f(100)=答案是2+或2 - 2根号2
已知f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|≤π/2)是定义域为R的奇函数,且当x=2时,f(x)取得最大值2,则
则f(1)+f(2)+f(3)+…+f(100)=
答案是2+或2 - 2根号2
已知f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|≤π/2)是定义域为R的奇函数,且当x=2时,f(x)取得最大值2,则则f(1)+f(2)+f(3)+…+f(100)=答案是2+或2 - 2根号2
已知f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|≤π/2)是定义域为R的奇函数,且当x=2时,f(x)取得最大值2,则f(1)+f(2)+f(3)+…+f(100)=
解析:∵f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|≤π/2)是定义域为R的奇函数
∴φ=0,∴f(x)=Asin(ωx)
∵当x=2时,f(x)取得最大值2
f(2)=Asin(2ω)=2==>A=2,sin(2ω)=1==>2ω=π/2==>ω=π/4
∴f(x)=2sin(π/4x)
f(1)=2sin(π/4)=√2,f(2)=2sin(π/4*2)=2,f(3)=2sin(π/4*3)=√2,f(4)=2sin(π/4*4)=0,f(5)=2sin(π/4*5)=-√2,f(6)=2sin(π/4*6)=-2,f(7)=2sin(π/4*7)=-√2,f(8)=2sin(π/4*8)=0
f(1)+f(2)+f(3)+…+f(8)=0
f(1)+f(2)+f(3)+…+ f(96)+ f(97)+ f(98)+ f(99)+f(100)
=f(97)+ f(98)+ f(99)+f(100)=√2+2+√2+0=2+2√2