Dear Colleagues,
I would like to expand the function (1-x)/(1-y) about (x=0; y=0) with x/y argument of the expansion. x and y are definite positive.
Any suggestion?
Thanks
Sandro
I note t=x/y. I obtain (1-x)/(1-y)=1/(1-y)-yt/(1-y). As y is close to 0, I obtain the approximation: (1-x)/(1-y)=1-yt. Is this approximation useful?
Thanks for your answer. However, your approximation is not useful since it still involves one of the original variable, i.e. y. I need an approximation where, for x->0 and y->0, the original function becomes f(t).
Sincerely
Sandro
As you have a function f(x,y)=(1-x)/(1-y) of 2 variables, it is not possible in this case to express the function only using t=x/y. What you want it is not possible in the general case. Indeed, the knowledge of t=x/y is not sufficient to know f. Suppose t=10, so x=10y. If y=0.1, x=1, so f=0. If y=0.01, x=0.1, so f=0.9/0.99=90/99=10/11=0.90909... If y decreases, f becomes closer to 1.
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