- #1
gipc
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- 0
Let F(x,y,z) be a function which is defined in the point M_0(x_0,y_0,z_0) and around it and the following conditions are satisfied:
1. F(x_0,y_0,z_0)=0
2. F has continuous partial derivatives in M_0 and around it
3. F'_z(x_0,y_0,z_0)=0
4. gradF at (x_0,y_0,z_0) != 0
5. It is known that there is a function f(x,y) so that F(x,y,f(x,y)) =0 in M_0 and around it
Prove that f(x,y) is differentiable in (x_0, y_0)
1. F(x_0,y_0,z_0)=0
2. F has continuous partial derivatives in M_0 and around it
3. F'_z(x_0,y_0,z_0)=0
4. gradF at (x_0,y_0,z_0) != 0
5. It is known that there is a function f(x,y) so that F(x,y,f(x,y)) =0 in M_0 and around it
Prove that f(x,y) is differentiable in (x_0, y_0)