Problem with directional derivative

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Discussion Overview

The discussion revolves around the existence of the directional derivative of a two-variable function at the point {0,0}. The function is defined as zero at this point and as (x^3 y^2)/(x^2 + Abs(y)^(2a)) elsewhere. Participants are exploring the conditions under which the directional derivative exists along a given vector and the value of the derivative when it exists.

Discussion Character

  • Homework-related, Exploratory, Debate/contested

Main Points Raised

  • One participant presents a problem involving a two-variable function and seeks to determine for which values of "a" the directional derivative exists at the origin.
  • Another participant questions whether the original post constitutes homework, suggesting that it resembles typical homework problems.
  • A further response clarifies the definition of homework in this context, indicating that a structured approach is expected for problem-solving.
  • There is a suggestion that using a specific homework template could facilitate clearer communication and understanding among participants.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the original post is homework. There is a general agreement on the need for a structured approach to the problem, but no agreement on the specifics of the problem-solving process or the conditions for the directional derivative.

Contextual Notes

Participants have not provided specific definitions or mathematical steps related to the directional derivative, and there is uncertainty regarding the necessary limits to be evaluated.

TonyEsposito
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Hi guys! i have a problem, and I'm unable to solvie it :/
I have this two variable function: it is 0 in {0,0} while it is (x^3 y^2)/(x^2+Abs(y)^(2a)) elsewhere.
do...given the vector {l1,l2} they are asking me: for which "a" the directional derivative along that vector exist in {0,0}? and when it exist what it is? Despite the fact that i know the background theory I'm unable to do the problem, in particular I'm unable to complete the necessary limit :/
 
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TonyEsposito said:
Hi guys! i have a problem, and I'm unable to solvie it :/
I have this two variable function: it is 0 in {0,0} while it is (x^3 y^2)/(x^2+Abs(y)^(2a)) elsewhere.
do...given the vector {l1,l2} they are asking me: for which "a" the directional derivative along that vector exist in {0,0}? and when it exist what it is? Despite the fact that i know the background theory I'm unable to do the problem, in particular I'm unable to complete the necessary limit :/
Is this homework?
 
what do u mean by homework?
 
TonyEsposito said:
what do u mean by homework?
Like - you are taking a course and you have been given some problems to solve .
 
The question looks like as if the homework template should have been used. If you start a thread there - in this case in
https://www.physicsforums.com/forums/calculus-and-beyond-homework.156/
then the template will automatically be applied:

Homework Statement


...

Homework Equations


...

The Attempt at a Solution


...
Thus, e.g. the definition of the directional derivative would be expected in section 2 and some effort from your side to solve the problem in section 3, i.e. where exactly did you get stuck and why. This is not meant to peeve you! It is meant to lay a common basis on which we can solve the problem together. Don't forget this is internet and the chances are high, that we might misunderstand each other. So the template serves the function of clarification.
 
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