investigating and finding the sensitivity

[akerman]

I have a question about function F(x) = sqrt(x)

I found that it has Kappa value equal to 1/2
I am not too sure what happens if when x = 0 is it just a minimum?

But now I am trying to investigate and find the sensitivity of F(x) to errors in x when we use x+ϵ, where ϵ is small. Any ideas how it can be done?

 

[Deleted member 4993]

I have a question about function F(x) = sqrt(x)

I found that it has Kappa value equal to 1/2
I am not too sure what happens if when x = 0 is it just a minimum?

But now I am trying to investigate and find the sensitivity of F(x) to errors in x when we use x+ϵ, where ϵ is small. Any ideas how it can be done?

Use Taylor series expansion of (x+ ε)^1/2 → x^1/2 [ 1 + (ε/x)]^1/2

 

[akerman]

Use Taylor series expansion of (x+ ε)^1/2 → x^1/2 [ 1 + (ε/x)]^1/2

I still don't get it ?
So what is the sensitivity of yfto errors in x?
And if we consider limit x→0, how many digits can one compute x√ when x is known to an error of 10−16?

 

[Deleted member 4993]

I still don't get it ?
So what is the sensitivity of yfto errors in x?
And if we consider limit x→0, how many digits can one compute x√ when x is known to an error of 10⁻¹⁶?

Can you please tell us the definition of error as it was explained to you (in your class, in your textbook, etc.)?

Do you know that the maximum error in truncating the Taylor series is the leading term of the |Remainder|?