Finding A Relative Condition Number

[ver_mathstats]

Homework Statement

Find the relative condition number for f(x)=sqrt(x+1)-sqrt(x).

Relevant Equations

f(x)=sqrt(x+1)-sqrt(x).

Hm I'm new to these concepts, and I want to make sure I am on the right track, would the relative condition number be:

k=(x/2)((1/sqrt(x+1))-(1/sqrt(x))(1/(sqrt(x+1)-sqrt(x))). Or would I have to solve the limit as x approaches 0?

Thank you.

 

[anuttarasammyak]

I know condition number in numerical analysis but what is the concept or definition of "relative condition number" you say?

 

[Mark44]

Homework Statement:: Find the relative condition number for f(x)=sqrt(x+1)-sqrt(x).
Relevant Equations:: f(x)=sqrt(x+1)-sqrt(x).

Hm I'm new to these concepts, and I want to make sure I am on the right track, would the relative condition number be:

k=(x/2)((1/sqrt(x+1))-(1/sqrt(x))(1/(sqrt(x+1)-sqrt(x))). Or would I have to solve the limit as x approaches 0?

Thank you.

1. I'm reasonably sure your equation above is written correctly, but it's really hard to parse.
2. I'm not familiar with the term "relative condition number," but this wikipedia article (https://en.wikipedia.org/wiki/Condition_number) provides a definition. The section titled "Several variables" defines the term "relative condition number."
3. From the above definition, the limit is on $\delta x$, not x.