f(x)=2sinx+1,(1)设常数ω>0,若y=f(ωx)在区间【-π/2,2π/3】上是增函数,求ω的取值范围(2)设集合A={π/6

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/12 08:39:20

f(x)=2sinx+1,(1)设常数ω>0,若y=f(ωx)在区间【-π/2,2π/3】上是增函数,求ω的取值范围(2)设集合A={π/6
f(x)=2sinx+1,(1)设常数ω>0,若y=f(ωx)在区间【-π/2,2π/3】上是增函数,求ω的取值范围
(2)设集合A={π/6

f(x)=2sinx+1,(1)设常数ω>0,若y=f(ωx)在区间【-π/2,2π/3】上是增函数,求ω的取值范围(2)设集合A={π/6
(1)解析:∵f(x)=2sinx+1
F(ωx)=2sinωx+1
∵在区间[-π/2,2π/3]上是增函数
∵函数f(x)初相为0
∴最小值点在Y轴左,最大值点在Y轴右,二者与Y轴之距相等
函数f(x)最小值点:ωx=2kπ-π/2==>x=2kπ/ω-π/(2ω)
∴-π/(2ω)-1/(2ω)ωx=2kπ/ω+π/(2ω)
π/(2ω)>=2π/3==>1/(2ω)>=2/3==>ω

(1)y=f(ωx)=2sinωx+1
递增区间在[-π/2ω,π/2ω]
那么就有-π/2ω≤-π/2且π/2ω≥2π/3
得到ω≤3/4
题目已知ω>0
所以0<ω≤3/4
(2)
g(x)=f(x)+m=0
sinx=-(1+m)/2
x∈[-π/6,7π/3]
sin(-π/6)=-1/2
sin(7...

全部展开

(1)y=f(ωx)=2sinωx+1
递增区间在[-π/2ω,π/2ω]
那么就有-π/2ω≤-π/2且π/2ω≥2π/3
得到ω≤3/4
题目已知ω>0
所以0<ω≤3/4
(2)
g(x)=f(x)+m=0
sinx=-(1+m)/2
x∈[-π/6,7π/3]
sin(-π/6)=-1/2
sin(7π/3)=√3/2
画图可知√3/2将sinx=-(1+m)/2代入得到
0<m<4

收起