Корень из 1-х2 найти область значений
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Ответил Alexandr130398
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E(y) - область значений
![y= sqrt{1- x^{2} } \ \y'= frac{1}{2 sqrt{1- x^{2} } } *(-2x)=- frac{x}{ sqrt{1- x^{2} } } \ \(-1)+++0---1 textgreater \ \ x_{min}=-1 = textgreater y_{min}= sqrt{1-(-1)^2} =0\ \ x_{min}=1 = textgreater y_{min}= sqrt{1-1^2} =0\ \ x_{max}=0 = textgreater y_{max}= sqrt{1-0^2} =1\ \ OTBET: E(y)=[0;1]](https://tex.z-dn.net/?f=y%3D+sqrt%7B1-+x%5E%7B2%7D+%7D+%5C+%5Cy%27%3D+frac%7B1%7D%7B2+sqrt%7B1-+x%5E%7B2%7D+%7D+%7D+%2A%28-2x%29%3D-+frac%7Bx%7D%7B+sqrt%7B1-+x%5E%7B2%7D+%7D+%7D+%5C+%5C%28-1%29%2B%2B%2B0---1+textgreater++%5C+%5C+x_%7Bmin%7D%3D-1+++%3D+textgreater++y_%7Bmin%7D%3D+sqrt%7B1-%28-1%29%5E2%7D+%3D0%5C+%5C+x_%7Bmin%7D%3D1+++%3D+textgreater+++y_%7Bmin%7D%3D+sqrt%7B1-1%5E2%7D+%3D0%5C+%5C+x_%7Bmax%7D%3D0++%3D+textgreater++y_%7Bmax%7D%3D+sqrt%7B1-0%5E2%7D+%3D1%5C+%5C+OTBET%3A+E%28y%29%3D%5B0%3B1%5D%0A "y= sqrt{1- x^{2} } \ \y'= frac{1}{2 sqrt{1- x^{2} } } *(-2x)=- frac{x}{ sqrt{1- x^{2} } } \ \(-1)+++0---1 textgreater \ \ x_{min}=-1 = textgreater y_{min}= sqrt{1-(-1)^2} =0\ \ x_{min}=1 = textgreater y_{min}= sqrt{1-1^2} =0\ \ x_{max}=0 = textgreater y_{max}= sqrt{1-0^2} =1\ \ OTBET: E(y)=[0;1]")
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