Multivariable Function Limit by Squeeze Theorem

[Peacefulchaos]

I have uploaded my question along with all of my work to Google Docs as a PDF, it can be found https://docs.google.com/fileview?id...1ZDktZmVlYjA4MTQxNzE2&hl=en&authkey=CL-llawP", which is why I did not follow the template provided. (I already had it in a PDF :$)

I am curious if it is appropriate to assume that r^2*cos^4(theta) goes to zero when I am trying to find the minimum of the denominator. (You will see what I am talking about once you get to the step.) If you don't follow my work I'll be happy to explain my thought process.

 

[benorin]

Your work is perfect, the assumption is valid since | \cos\theta | \le 1 and likewise for the sine function. You can save some work by working the inequality a little before switching polar.