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squenshl
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Why is it not possible to find a function g such that g [tex]\in[/tex] C1 at (0,0) and g is not differentiable at (0,0)
squenshl said:Why is it not possible to find a function g such that g [tex]\in[/tex] C1 at (0,0) and g is not differentiable at (0,0)
squenshl said:Also given that f(x,y) = x|y| how do I show that f [tex]\notin[/tex] C1 at (0,0)
Yes, it is not possible to find a function g in certain cases. There are many mathematical problems that have been proven to have no solution or no function that can accurately solve them. This can be due to the complexity of the problem or limitations in our current understanding and technology.
There are many reasons why it may not be possible to find a function g. It could be because the problem is unsolvable, the data is insufficient, or the variables involved are too complex. It could also be due to limitations in our knowledge and understanding of mathematics.
In theory, we could keep searching for a function g, but there is no guarantee that we will find one. Some problems are proven to be unsolvable, and no amount of searching will change that. It is also important to consider the time and resources required for such a search, which may not be feasible.
Yes, there are alternative approaches to solving problems that do not involve finding a function g. These may include using approximation methods, numerical methods, or even changing the problem to make it solvable. It is important to consider all options when faced with a problem that seems impossible to solve.
It is impossible to say for certain if it will ever be possible to find a function g for a particular problem. As our knowledge and technology continue to advance, it is possible that we may find a solution or a function that can accurately solve the problem. However, there may also be problems that are fundamentally unsolvable, and in those cases, it will never be possible to find a function g.