[tex-k] mathematical error in Appendix D of The METAFONTbook

Tue Oct 27 15:37:49 CET 2020

```Page 293 of The METAFONTbook says

When c -> 0, the quantity a^3 + b^3 approaches [negative infinity]
when c is negative, [positive infinity] when c is positive.

However, a Maxima session reveals that the opposite is the case:

(%i1) solve([-2*a+3*b/c=c-3, a*c+2*b=c^3-20], [a,b]);
3      2                    3    2
3 c  - 2 c  + 6 c - 60      2 c  + c  - 3 c - 40
(%o1)      [[a = ----------------------, b = --------------------]]
7 c                         7
(%i2) x: ev(a^3+b^3, %o1);
3      2            3       3    2            3
(3 c  - 2 c  + 6 c - 60)    (2 c  + c  - 3 c - 40)
(%o2)         ------------------------- + -----------------------
3                       343
343 c
(%i3) limit(x, c, 0, minus);
(%o3)                                 inf
(%i4) limit(x, c, 0, plus);
(%o4)                                minf
(%i5) x, c=-0.1;
(%o5)                          649376.0118656126
(%i6) x, c=-0.01;
(%o6)                        6.316349304804057E+8
(%i7) x, c=0.1;
(%o7)                         - 611749.196040469
(%i8) x, c=0.01;
(%o8)                       - 6.278566626283495E+8
(%i9)

Can someone verify?

----

Previous reports:
https://github.com/dine2014/texbook-mfbook-bugs/blob/master/bugs.md

```