10 REM function approximation by Newton's Method
20 REM Frank G. Kienast January, 1986
25 REM MODIFIED FOR TANDY 102 SEPTEMBER, 1986
27 REM COMPUSERVE USER [73327,3073]
30 REM Y=f(X)=0 defined in lines 1000-1999
35 NI=30
37 CLS
40 INPUT"Enter initial guess for X";X0
50 X=X0
60 N=0
70 GOSUB 1000
80 IF ABS(Y)<.00001 THEN 210
90 N=N+1
92 IF N>NI THEN 410
95 YTEMP=Y
100 XTEMP=X
110 X=X+.00001
120 GOSUB 1000
130 DY=(Y-YTEMP)/.00001
140 X=X-Y/DY
150 GOTO 70
210 REM Found value for Y
260 PRINT N;"iterations were required."
265 PRINT"X=";
290 IF X<0 THEN SIGN=-1 ELSE SIGN=1
300 LET X3=ABS(X)
310 LET X4=INT(100000!*X3+.5)/100000!
320 PRINT SIGN*X4
350 STOP
410 REM No answer
450 PRINT"The function did not converge
460 PRINT"in";NI;"iterations."
470 STOP
1000 REM define Y=f(X)=0 here
1010 LET Y=SIN(X)-3*COS(X)^2 'Example
1999 RETURN
9999 END