REM *******************************************

REM *       NEWTON'S METHOD ILLUSTRATION      *

REM *******************************************

DEFDBL A-Z

SCREEN 11

REM COLOR 11, 7

X0 = 20: Y0 = 90: KY = 40 / 10000: KX = 600 / 20

LINE (X0, 50)-(X0, 450)

LINE (X0, Y0)-(620, Y0)

CIRCLE (X0 + KX * 10, Y0 - KY * (10000 - (10 ^ 5))), 5

LINE (X0, 50)-(X0, 50)

FOR I = 1 TO 15 STEP .1

F1 = 10000 - I ^ 5

Y1 = F1 * KY

LINE -(X0 + (I * KX), Y0 - (Y1))

NEXT

XAP2 = 10: SLOP = 1

100 XAPP = XAP2: DELX = (10000 - XAPP ^ 5) / (SLOP * 1000000!)' START NEWTON'S APPROXIMATION HERE

YAPP = 10000 - XAPP ^ 5

YAPD = 10000 - (XAPP + DELX) ^ 5

DELY = (YAPD - YAPP)

SLOP = DELY / DELX

XAP2 = XAPP - (YAPP / SLOP)

YAP2 = 10000 - XAP2 ^ 5

LINE (X0 + (XAPP * KX), Y0 - (YAPP * KY))-(X0 + (XAP2 * KX), Y0)

LINE -(X0 + (XAP2 * KX), Y0 - (YAP2 * KY))

IF ABS(YAP2) > .000001 THEN 100

CIRCLE (X0 + KX * XAP2, Y0 - KY * (10000 - (XAP2 ^ 5))), 5

LOCATE 24, 3: PRINT "BEGINNING ESTIMATE = 10"

LOCATE 25, 3: PRINT "ENDING ESTIMATE = "; XAP2

LOCATE 26, 3: PRINT "ACTUAL VALUE F(X) = "; YAP2

LOCATE 27, 2

INPUT "ENTER TO END"; A$

END





