Re: to determine a root of f(x)=0 that is accurate within a specified tolerance value
Surely the subject here is using numerical methods to estimate roots.
For example, if the root is 3, then:
Numbers between 2.9 and 3.1 are accurate within a tolerance of 0.1
Numbers between 2.99 and 3.01 are accurate within a tolerance of 0.01
Numbers between 2.999 and 3.001 are accurate within a tolerance of 0.001
...
They're not exactly accurate, but they are close enough given the tolerance level.
In the case of an irrational root, like pi, you will never come up with an exactly accurate numerical representation, so you have to satisfy yourself with approximations of varying accuracy. In the case of pi, 3.14159 is more accurate than 3.14.
NOT A TEACHER. Translator and editor, and I hold a TESOL certificate. Native speaker of American English (West Coast)