设函数f(x)=sinwx(w>0)在区间[-π/5,π/3]上是增函数,则w的取值范围是
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![设函数f(x)=sinwx(w>0)在区间[-π/5,π/3]上是增函数,则w的取值范围是](/uploads/image/z/8238152-56-2.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dsinwx%28w%3E0%29%E5%9C%A8%E5%8C%BA%E9%97%B4%5B-%CF%80%2F5%2C%CF%80%2F3%5D%E4%B8%8A%E6%98%AF%E5%A2%9E%E5%87%BD%E6%95%B0%2C%E5%88%99w%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AF)
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设函数f(x)=sinwx(w>0)在区间[-π/5,π/3]上是增函数,则w的取值范围是
设函数f(x)=sinwx(w>0)在区间[-π/5,π/3]上是增函数,则w的取值范围是
设函数f(x)=sinwx(w>0)在区间[-π/5,π/3]上是增函数,则w的取值范围是
f(x)=sinwx是奇函数,图象关于原点对称
由-π/2≤wx≤π/2 ==> -π/(2w)≤x≤π/(2w)
∴f(x)在原点附近单调递增区间为
[-π/(2w),π/(2w)]
f(x)=sinwx在区间[-π/5,π/3]上是增函数
[-π/5,π/3]被包含于[-π/(2w),π/(2w)]
∴π/5≤π/(2w)且π/3≥π/(2w)
∴2/3≤w≤5/2