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mathmari
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MHB
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Hi!
Which is the parametrization of z= y^2-x^2 , and f(x,y)=(-x,-y,z) ?
Which is the parametrization of z= y^2-x^2 , and f(x,y)=(-x,-y,z) ?
HallsofIvy said:I don't understand what "f(-x, -y, z)" has to do with this. What is "f"?
mathmari said:I don't really know...It is given from the exercise :(
mathworker said:\(\displaystyle y=(1+t)^2\)
\(\displaystyle x=(1-t)^2\)
\(\displaystyle z=4t...\)
may be?
I like Serena said:Looks to me as if you're supposed to give a parametrization in the form f(x,y).
In that case your parametrization would be:
$$f(x,y)=(-x,-y,y^2-x^2)$$
mathworker said:\(\displaystyle y=(1+t)^2\)
\(\displaystyle x=(1-t)^2\)
\(\displaystyle z=4t...\)
may be?
yes!mathmari said:You mean:
\(\displaystyle y^2=(1+t)^2\)
\(\displaystyle x^2=(1-t)^2\)
\(\displaystyle z=4t\)
Right??
Parametrizing a function means representing the function using a set of parameters or variables. This allows us to express the function in terms of these parameters, making it easier to work with and analyze.
To parametrize a function, we need to choose a set of parameters that can represent the function. For the function Z=y^2-x^2, we can choose the parameters x and y themselves, since they already appear in the function. This gives us the parametrization Z(x,y)=y^2-x^2.
Parametrizing a function can make it easier to study and analyze. It can also help in visualizing the function and understanding its behavior. Parametrization can also be useful in solving problems involving the function and in finding specific values or solutions.
To parametrize a vector function, we need to assign parameters to each component of the vector. In this case, we can choose x and y as parameters for the first two components and z as the parameter for the third component. This gives us the parametrization f(x,y,z)=(-x,-y,z).
Yes, any function can be parametrized as long as we can find a suitable set of parameters that can represent the function. However, some functions may be more difficult to parametrize than others and may require more complex parameters.