# limits

• April 1st 2008, 04:02 AM
samdmansam
limits
find lim (x,y) aproach(0,0) 2xy/((x^2)+2y^2 if it exists, explain why the limit does or does not exist

Use polar coordinates to find lim(x,Y)approach(0,0)
(sin(x^2+y^2))/(x^2+y^2)
• April 1st 2008, 05:08 AM
mr fantastic
Quote:

Originally Posted by samdmansam
find lim (x,y) aproach(0,0) 2xy/((x^2)+2y^2 if it exists, explain why the limit does or does not exist

Mr F asks: What value do you get if you approach (0, 0) along the line y = mx ....? Therefore .....

Use polar coordinates to find lim(x,Y)approach(0,0)
(sin(x^2+y^2))/(x^2+y^2)

Mr F says: Then go to polars!: ${\color{red}\lim_{r \rightarrow 0} \frac{\sin r^2}{r^2} = \lim_{t \rightarrow 0} \frac{\sin t}{t} = .....}$

..