已知f(x)连续可导,证明g((x,y),(a,b))亦连续.已知f(x)在(-pi/2,pi/2)上连续可导,定义g(x,y)在集合E:=(-pi/2,pi/2)*(-pi/2,pi/2),g(x,y)=[f(x)-f(y)]/[sin(x)-sin(y)],证明g(x,y)在E上连续.
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![已知f(x)连续可导,证明g((x,y),(a,b))亦连续.已知f(x)在(-pi/2,pi/2)上连续可导,定义g(x,y)在集合E:=(-pi/2,pi/2)*(-pi/2,pi/2),g(x,y)=[f(x)-f(y)]/[sin(x)-sin(y)],证明g(x,y)在E上连续.](/uploads/image/z/12510483-51-3.jpg?t=%E5%B7%B2%E7%9F%A5f%28x%29%E8%BF%9E%E7%BB%AD%E5%8F%AF%E5%AF%BC%2C%E8%AF%81%E6%98%8Eg%28%28x%2Cy%29%2C%28a%2Cb%29%29%E4%BA%A6%E8%BF%9E%E7%BB%AD.%E5%B7%B2%E7%9F%A5f%28x%29%E5%9C%A8%28-pi%2F2%2Cpi%2F2%29%E4%B8%8A%E8%BF%9E%E7%BB%AD%E5%8F%AF%E5%AF%BC%2C%E5%AE%9A%E4%B9%89g%28x%2Cy%29%E5%9C%A8%E9%9B%86%E5%90%88E%3A%3D%28-pi%2F2%2Cpi%2F2%29%2A%28-pi%2F2%2Cpi%2F2%29%2Cg%28x%2Cy%29%3D%5Bf%28x%29-f%28y%29%5D%2F%5Bsin%28x%29-sin%28y%29%5D%2C%E8%AF%81%E6%98%8Eg%28x%2Cy%29%E5%9C%A8E%E4%B8%8A%E8%BF%9E%E7%BB%AD.)
已知f(x)连续可导,证明g((x,y),(a,b))亦连续.已知f(x)在(-pi/2,pi/2)上连续可导,定义g(x,y)在集合E:=(-pi/2,pi/2)*(-pi/2,pi/2),g(x,y)=[f(x)-f(y)]/[sin(x)-sin(y)],证明g(x,y)在E上连续.
已知f(x)连续可导,证明g((x,y),(a,b))亦连续.
已知f(x)在(-pi/2,pi/2)上连续可导,定义g(x,y)在集合E:=(-pi/2,pi/2)*(-pi/2,pi/2),
g(x,y)=[f(x)-f(y)]/[sin(x)-sin(y)],
证明g(x,y)在E上连续.
已知f(x)连续可导,证明g((x,y),(a,b))亦连续.已知f(x)在(-pi/2,pi/2)上连续可导,定义g(x,y)在集合E:=(-pi/2,pi/2)*(-pi/2,pi/2),g(x,y)=[f(x)-f(y)]/[sin(x)-sin(y)],证明g(x,y)在E上连续.
函数f(x)=tanx,y=f(π/2-x)sinx=tan(π/2-x)sinx
=[sin(π/2-x)/cos(π/2-x)]*sinx=cosx*sinx/sinx=cosx
定义域sinx≠0,则cosx≠±1所以图像是cosx的一部分,
且要去掉X=0和X=π这二点,如图所示;
向左转|向右转
函数f(x)=tanx,y=f(π/2-x)sinx=tan(π/2-x)sinx =[sin(π/2-x)/cos(π/2-x)]*sinx=cosx*sinx/sinx=cosx 定义域sinx≠0,则cosx≠±1所以图像是cosx的一部分, 且要去掉X=0和X=π这二点,如图所示; 向左转|向右转