Is this solution to a limit equation correct?

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nedfin
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Homework Statement
I ran into this equation online and an interested in why my answer might be wrong. What if anything is wrong with my logic.
Relevant Equations
1-(1/((x-y)^x))
lim(x,y) -> (inf,0)
Why is this not equivalent to

1 - inf^-inf,

Or 1 - infinitesimal ,

Or 1 ?

My answer was 1, which I told is incorrect.
 
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<br /> \lim _{(x,y)\to (\infty,0)} \frac{1}{(x-y)^{x}} = 0<br />
because ##(x-y)^x \to \infty ## as ##(x,y)\to (\infty,0)##. It is not equivalent to the first two items. ##\infty ^{-\infty}## is not a thing and neither is "infinitesimal". The initial limit is ##1## as you say.
 
nuuskur said:
<br /> \lim _{(x,y)\to (\infty,0)} \frac{1}{(x-y)^{x}} = 0<br />
because ##(x-y)^x \to \infty ## as ##(x,y)\to (\infty,0)##. It is not equivalent to the first two items. ##\infty ^{-\infty}## is not a thing and neither is "infinitesimal". The initial limit is ##1## as you say.
Thanks
 
nedfin said:
Homework Statement:: I ran into this equation online and an interested in why my answer might be wrong. What if anything is wrong with my logic.
Relevant Equations:: 1-(1/((x-y)^x))
lim(x,y) -> (inf,0)

Why is this not equivalent to

1 - inf^-inf,

Or 1 - infinitesimal ,

Or 1 ?

My answer was 1, which I told is incorrect.
Welcome to PF. :smile: I'm glad that @nuuskur was able to help you.

BTW, please consider learning LaTeX to post equations in discussion forums. You can find a "LaTeX Guide" link at the bottom of the Edit Window. It makes math equations *much* easier to read (as you can see by nuuskru's post). :smile:
 
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