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.

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# Limits and continuity

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