sine function from 0 to PI

  coefficients
    0.000000    0.985330    0.052480   -0.233079    0.037096

        x          f(x)      polynomial
    0.157080     0.156434     0.155189
    0.471239     0.453990     0.453418
    0.785398     0.707107     0.707443
    1.099557     0.891007     0.891247
    1.413717     0.987688     0.987485
    1.727876     0.987688     0.987485
    2.042035     0.891007     0.891247
    2.356194     0.707107     0.707443
    2.670354     0.453991     0.453418
    2.984513     0.156434     0.155189

************************************
press RETURN
exponential function from 0 to 1

  coefficients
    1.000532    0.994006    0.524018    0.123288    0.076437

        x          f(x)      polynomial
    0.050000     1.051271     1.051558
    0.150000     1.161834     1.161878
    0.250000     1.284025     1.284010
    0.350000     1.419068     1.419060
    0.450000     1.568312     1.568318
    0.550000     1.733253     1.733258
    0.650000     1.915541     1.915536
    0.750000     2.117000     2.116994
    0.850000     2.339647     2.339656
    0.950000     2.585710     2.585727

************************************
press RETURN