In general, that is not always true (that is, lim|f(x,y)| does not always equal lim f(x,y)). It only works here because the limit is zero. Intuitively, this should make sense - the only way |f(x,y)| can approach zero (get smaller) is if f(x,y) itself were approaching zero. For a more formal proof, use the squeeze theorem: -|f(x,y)|
i was literally trying to find the solution to this specific limit problem, and only found it because it was in the thumbnail. thank you are a godsend
This video explained it better than any other video. Thx
Thank you, I took this theorem 3 times in school and uni, and I just now I understood it ❤️
Thanks for you video Brother. Greetings from Chile
Keep it up bro
very clear and helpful :)
why do you take the absolute value?
Thanks for this video! Can you help me understand Mark, why the last part is true? lim|f(x,y)| = limf(x,y) ?
In general, that is not always true (that is, lim|f(x,y)| does not always equal lim f(x,y)).
It only works here because the limit is zero. Intuitively, this should make sense - the only way |f(x,y)| can approach zero (get smaller) is if f(x,y) itself were approaching zero. For a more formal proof, use the squeeze theorem: -|f(x,y)|
@@moocow212 oh, now I got it ! Thanks for your explanation. Math and people learning it are great ))