- #1

negation

- 818

- 0

Suppose the lim

_{(x,y) →(0,0) (xy)/SQRT[x^2 + y^2] if it exists find the limit. The Attempt at a Solution x = rcosΘ y = r sinΘ r = SQRT[x^2 + y^2] ∴ limr → 0 (r2cosΘrsinΘ)/ r = rcosΘsinΘ [itex]\leq r[/itex] and so -r [itex]\leq(xy)/SQRT[x^2 + y^2][/itex] [itex]\leq r[/itex] ... ... 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 [itex]\leqr[/itex]?}