Recent content by Kenneth1997

a better understanding should be the goal not solving homework to high schoolers imo. i already demonstrated what you did so i don't think you are showing more then you should have.

but how do i demonstrate it?

edited,yep i meant the second

Homework Statement study the continuity, directional derivatives, and differentiability of the function f(x,y)=arctan(abs(y)*(y+x^2-1)). The Attempt at a Solution the function is obviously continuous in R2 since made of continuous functions. has directional derivatives everywhere since made...

i think he just mean a generic direction

i explained myself horribly. what I am asking is: there is a way to know when the directional derivatives don't exist?

what do you mean with more then one limit? im not familiar with the terminology, I am not a native english speaker, you mean the "gradient formula"?

x*abs(y)*(y+x^2+x)=f(x,y) so, on normal points they are tangent vectors on some point in the chosen direction. how about in critical points, where there shouldn't be any on a geometrical standpoint? can i say they exist if i get them with the definition? or the result i get has no value? like...

hey guys, I am a student of mathematical engineering, hope i will be able to improve mine and your knowledge

it wouldn't even be possible for the function i was trying to solve, and certainly it wouldn't help for finding a limit

what you are saying is what i have been saying since my first comment. mark is saying that converting to the polar form we are talking about considers also NON linear paths (i never said that the polar form didnt consider linear paths as you implied), which is the opposite as what you have...

everything you are saying is correct, every single word. but now you are going against mark44, because he says that the polar form includes also paths that are not straight lines.

hope you didnt register to this forum just for this

thanks man, this should do the trick still think it doesn't include linear paths, or the theta would be a variable not a constant, and in that case you couldn't treat it anymore as a one variable limit and you have the same problem as before. btw, theta still appears in the function i was...

cant i just say the function is > then f(x,y)=(ln(1+x)/(x^4)) that goes to +inf and so my function goes to +inf aswell?