IIT JEE , AIEEE Forum - Mathematics , Algebra

pardesi

no that's not true S can be considered as a function in each variable seperately holding out others constant and in each case it is continiouas at each point in the reals - the point where it blows up
also it's clear that 1<=S<=2
we now prove that one can get as close one wants to both of them
set a=b=u and c=d=v
now take the limit x--->1 and y--->0 along any path u want(if u wnat them to go depenedently otherwise no prob)(as the cauchy-reimann conditions hold true)
we get the limit as 1
set a=c=u and b=d=v and take limits as u--->1 and v--->0if u wnat them to go depenedently otherwise no prob) we get limit as 2
so we can get arbitrarily close

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