Using polar corrdinates, evaluate so , Since hence limit=0 Can I ask why is that so? when x,y goes to 0 respectively, which variable goes to 0? r or ?
Last edited by mr fantastic; October 17th 2009 at 05:03 PM. Reason: Improved the latex for better formatting.
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Originally Posted by noob mathematician Using polar corrdinates, evaluate Did you notice that it is in the denominator? Is that a typo? If not, the limit does not exist. Look at the path along the x-axis and the along the y-axis.
Do you mean If so, then using the Pythagorean identity , we obtain Now notice that is the variable that goes to (as we're approaching the origin), and Edit: Added more useful inequality.
Last edited by Scott H; October 17th 2009 at 07:24 AM.
Originally Posted by Plato Did you notice that it is in the denominator? Is that a typo? If not, the limit does not exist. Look at the path along the x-axis and the along the y-axis. Oh yeah it shd be y^2 Originally Posted by Scott H Do you mean If so, then using the Pythagorean identity , we obtain Now notice that is the variable that goes to (as we're approaching the origin), and Edit: Added more useful inequality. Oh so it's actually the r goes to 0 and not the ? Then by squeeze theorm we conclude it goes to 0 right?
Originally Posted by noob mathematician Oh so it's actually the r goes to 0 and not the ? Then by squeeze theorm we conclude it goes to 0 right? Correct. If goes to , our point approaches the -axis, but not necessarily the origin.
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