[tex-k] mathematical error in Appendix D of The METAFONTbook
胡亚捷 (Hu Yajie)
2500418497 at qq.com
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?
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