Numerical Analysis - Relative Error

Hi, I am working on the following problem and need some assistance:

For what range of values of x will the computed value of f(x) given below have large relative error? Assume 0 x 100

f(x) = 10 -

I know that catostrophic error can occur when subtracting two numbers of similar magnitude, so in our case would we present the most relative error when x is equal to 0 and 100? Or do I need a wider range of numbers?

Thanks

Quote:

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Originally Posted by jnava

Hi, I am working on the following problem and need some assistance:

For what range of values of x will the computed value of f(x) given below have large relative error? Assume 0 x 100

f(x) = 10 -

I know that catastrophic error can occur when subtracting two numbers of similar magnitude, so in our case would we present the most relative error when x is equal to 0 and 100? Or do I need a wider range of numbers?

Thanks

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Assume some reasonable relative error for the square root operation. See what happens for x1 which is close to 100, like 100 minus a few times the relative error times 100. Then see what happens with x2 = 100 - x1, which is a number close to zero.

Quote:

---

Originally Posted by jnava

Hi, I am working on the following problem and need some assistance:

For what range of values of x will the computed value of f(x) given below have large relative error? Assume 0 x 100

f(x) = 10 -

I know that catostrophic error can occur when subtracting two numbers of similar magnitude, so in our case would we present the most relative error when x is equal to 0 and 100? Or do I need a wider range of numbers?

Thanks

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With a simple step You obtain...

(1)

... and any criticity disappears. In particular for 'small' values of x is ...

Kind regards