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.
That is
the limit as f(x) as x->0 is 0, so you could set f(0)=0 to make this happen?
Is this correct?
Actually, it is
It is "continuous from the right" if you set f(0)= 0.All right!... but necessary condition for to be continous in is...
(2)
Is that satisfied for (1)? ...
Kind regards
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...
(1)
... 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...
(2)
... and I reported for semplicity sake one of them...
... You say 'many text books use' and that means automatically that 'many text books don't' anf that is enough to make your point of view a little questionable...
Kind regards