just checking...

[Sarahisme]

is this a 'proof' for this question?

 

[math]

h(x) = \sqrt(3 + x)

[/math]

 

we want to find a K > 0 such that

[math]

|h(x) - h(y)| \leq K|x-y| \forall x,y \in [0,1]

[/math]

 

that is we want a K > 0 such that

[math]

|\sqrt(3 + x) - \sqrt(3 + y)| \leq K|x-y| \forall x,y \in [0,1]

[/math]

 

now

[math]

|\sqrt(3 + x) - \sqrt(3 + y)| [/math]

[math]

= frac{|(\sqrt(3 + x) - \sqrt(3 + y))(\sqrt(3 + x) - \sqrt(3 + y)|}{1}

[/math]