1a)Do these functions have limits.If the limit exists, find it with justification, if not explain why not
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) ={2x sin y/ x²+y² if y >x
sin(x+y) if y≤x
Determine the points at which f is continuous.
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) ={2x sin y/ x²+y² if y >x
sin(x+y) if y≤x
Determine the points at which f is continuous.
