Set f: (0,1) --> R by:
f(x) = (1/sqrt(x))-sqrt((x+1)/(x))
Can one definite f(0) to make f continuous at ? Explain.
I believe you can set the limit as x approaches 0 equal to f(0) in order to make it continuous.
the limit as f(x) as x->0 is 0, so you could set f(0)=0 to make this happen?
Is this correct?
It is "continuous from the right" if you set f(0)= 0.All right!... but necessary condition for to be continous in is...
Is that satisfied for (1)? ...
And many text books use the term "continuous" to mean that if is a sequence of points in the domain of f converging to a, then .
In the complex z plain the function...
... is a multivalued function and in particular it has four independent branches connecting two branch points: and . When , real the four branches can be represented as...
... and I reported for semplicity sake one of them...