1a)Do these functions have limits.If the limit exists, find it with justification, if not explain why not(adsbygoogle = window.adsbygoogle || []).push({});

i) f(x,y) =x²-y²/x²+y²

ii) f(x,y) =x³-y³/x²+y²

iii) f(x,y) =xy/|x|+|y|

iv) f(x,y) =1-√(1-x²)/x²+ xy+y²

v) f(x,y) =y³x/y^6+x²

im having problems finding the limits especially iii) and iv). i know that you can prove a limit doesn't exist by demonstration but how do you justify it if it does exist

b) Let f be a real valued function of two real variables defined by:

f(x,y) ={2x² sin y/ x²+y² if y >x

sin(x+y) if y≤x

Determine the points at which f is continuous.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Limits and continuity

**Physics Forums | Science Articles, Homework Help, Discussion**