# Limits if polar coordinates (conceptual explanation)

1. Mar 29, 2014

### negation

1. The problem statement, all variables and given/known data[/b]

Suppose the lim(x,y) →(0,0) (xy)/SQRT[x^2 + y^2] if it exists

find the limit.

3. The attempt at a solution

x = rcosΘ
y = r sinΘ
r = SQRT[x^2 + y^2]

∴ limr → 0 (r2cosΘrsinΘ)/ r = rcosΘsinΘ $\leq r$

and so -r $\leq(xy)/SQRT[x^2 + y^2]$ $\leq r$

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I can understand the limit goes to zero because algerbraic multiplication and the sandwhich theorem tells me so. However, the highlighted part in red confuses me. What is the significance of
rcosΘsinΘ $\leqr$?

2. Mar 29, 2014

### UltrafastPED

It was to generate the inequality - they used cosΘrsinΘ ≤ 1.