RE: relation between repeated limit & double limit

[rohan saxena]

Easy method to find point of  inflexion of


r=b(theta^n)

Sent from my Windows Phone

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From: Sarita Math
Sent: 22-09-2012 23:52
To: tutori...@googlegroups.com
Subject: Re: relation between repeated limit & double limit

Here,

Similarly, 

Hence the repeated limits exist and they are equal.

Again, since there are points arbitrarily near (0,0) at which f is equal to 0 and points arbitrarily near (0,0) at which f is equal to 1. Therefore, for any ,

|f(x,y)-f(0,0)=|f(x,y)| 

for all points in any neighborhood of (0,0).

Hence,

    does not exist.

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[Sarita Math]

This problem was done in class.

putting , and then point of inflexion lie on,

[anuja gadekar]

ma'm,
  To find point of inflection we should equate double derivative of r to zero. How we are getting point of inflection by that condition( which is in terms of u) ?

[Sarita Math]

Anuja, Whatever you are saying that is for Cartesian coordinate i.e. equating the double derivative to 0. But for polar, in the class, we have introduced the variable u=1/r and also, I told that, to check convexity or concavity in polar coordinate, we have to check the sign of the term 

and point of inflexion lie on the curve by equating this term to 0.