The function ( )=1/(1 + 2 ) is to be approximated using a piecewise linear function ( ) over the interval 0 ≤   . The requirement is that | ( ) − ( )| ≤ 10 −4 for 0 ≤ . Explain how to determine the...

The function()=1/(1 +

²) is to be approximated using a piecewise linear function
() over the interval 0 ≤
. The requirement is that |() −
()| ≤ 10⁻⁴
for 0 ≤

. Explain how to determine the spacing of the


_i
’s used in the construction of
(), and how you handle the approximation over the intervals


_n

≤
 ≤


_n+1
and


_n+1
≤
, where


_n+1
is the largest node you use.