- #1
SqueeSpleen
- 141
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While I was doing exercises about this, I noticed that, for example [itex]f(x,y)=e^{x^2+y^2}[/itex] was very similar to [itex]f(x,y)=x^2+y^2[/itex]
And something similar with:
[itex]f(x,y)=e^{(1-x^2-y^2)^{(1/2)}}[/itex] and [itex]f(x,y)=(1-x^2-y^2)^{(1/2)}[/itex]
So I supposed that some transformations that preserves some properties kinda preserves also the shape of some functions.
So when I had to graph the function [itex]e^{1-x^2-y^2}[/itex] I explained that I draw something similar to a paraboloid, but the points that would be [itex]z \in (-\infty,0)[/itex] in a paraboloid, where in (0,1), the point of z = 0 was in 1, and the points [itex]z \in (0, \infty)[/itex] where in (1,∞), I think it's something like ploting the function in "logarithm scale".
I wouldn't put this explanation when it wasn't rigoruos at all, and I only was asked to sketch the function (I did this well :p), but this information was not only irrelevant but also wrong :P, so I lost points doing that.
I wanted to know how this is called and a formal explanation of this phenomenon because I didn't heard about this in class but I guess this was the sort of explanation I had to do about why I sketched that graph.
Offtopic questions I don't know where to ask or I guess they don'r deserve a new topic:
(*) What's the best online English-Spanish math dictionary?
(*) If you graph in a fixed area a hiperboloid, for example
x^2+y^2-1=z
with [itex]x \in (-a,a)[/itex] [itex]y \in (-a,a)[/itex] as "a" gets bigger, the graph of the hiperboloid will be closed to the graph of the cone x^2+y^2=z, same will happen with x^2+y^2+1=z
I guess same will happen with a lot of curves, not all, I think some curves with, for example trigonometric functions will never "converge".
There's some subject where this is studied? How it's called it?
And something similar with:
[itex]f(x,y)=e^{(1-x^2-y^2)^{(1/2)}}[/itex] and [itex]f(x,y)=(1-x^2-y^2)^{(1/2)}[/itex]
So I supposed that some transformations that preserves some properties kinda preserves also the shape of some functions.
So when I had to graph the function [itex]e^{1-x^2-y^2}[/itex] I explained that I draw something similar to a paraboloid, but the points that would be [itex]z \in (-\infty,0)[/itex] in a paraboloid, where in (0,1), the point of z = 0 was in 1, and the points [itex]z \in (0, \infty)[/itex] where in (1,∞), I think it's something like ploting the function in "logarithm scale".
I wouldn't put this explanation when it wasn't rigoruos at all, and I only was asked to sketch the function (I did this well :p), but this information was not only irrelevant but also wrong :P, so I lost points doing that.
I wanted to know how this is called and a formal explanation of this phenomenon because I didn't heard about this in class but I guess this was the sort of explanation I had to do about why I sketched that graph.
Offtopic questions I don't know where to ask or I guess they don'r deserve a new topic:
(*) What's the best online English-Spanish math dictionary?
(*) If you graph in a fixed area a hiperboloid, for example
x^2+y^2-1=z
with [itex]x \in (-a,a)[/itex] [itex]y \in (-a,a)[/itex] as "a" gets bigger, the graph of the hiperboloid will be closed to the graph of the cone x^2+y^2=z, same will happen with x^2+y^2+1=z
I guess same will happen with a lot of curves, not all, I think some curves with, for example trigonometric functions will never "converge".
There's some subject where this is studied? How it's called it?
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