What is the graphic of #f(x) = sqrt(x+sqrt(x+sqrt(x+sqrt(x+...))))# for #x ge 0#?
What is the graphic of #f(x) = sqrt(x+sqrt(x+sqrt(x+sqrt(x+...))))# for #x ge 0# ?
What is the graphic of
1 Answer
This is the continued-surd model for the equation of part of a parabola, in the first quadrant. Not in the graph, the vertex is at #(-1/4, 1.2) and the focus is at (0, 1/2).
Explanation:
As of now,
The graph is the part of a parabola that has vertex at
and latus rectum 4a = 1.. The focus is at
As
quadrant, wherein
I think it is better to restrict x as > 0, to avoid (0, 1) of the parabola.
Unlike parabola y, our y is single-valued, with
graph{(x+y-y^2)((x-4)^2+(y-2.56)^2-.001)=0[0.1 5 1 5] }
I make it for another g in continued-surd
Let g(x) = ln x. Then
Here,
graph{((ln x+y)^0.5-y)((x-1)^2+(y-1)^2-.01)=0[0..779 1 0.1 1] }