Mathematics

Problem

When estimating

\displaystyle \lim_{x\to a}f(x)

numerically from a table of values for

f

, which practice MOST directly reduces truncation error in the estimate? a) Averaging values of

f(x)

that are symmetric about

a

even if they are relatively far from

a

b) Using values of

x

that are as close to

a

as possible without causing loss of significant digits c) Reporting only the tabulated value

f(a)

, even if

a

is an endpoint of the table d) Comparing

f(a+1)

and

f(a-1)

because larger separations reduce round-off noise