~v200 200 ~w38 0 534 784 0 323 0 0 ~f? 14 12 10
? 2 0 1 0 ? ? ? "Arial" ? ? ? 0 ? 0 0
"Times" 12 ? ? 6 0 c n 102 0 0 0 k 288
i"NEWTONS  METHOD"
-2 1 26177 26178 26115 26178 1 1 1 1 0 0
0 0 -1 0 0 -1 -1 -1 -1 -1 1 1 ? ? 
~Q
]|Expr|[#b @`bb#_b#_b#_})8# b&P" *|: ;bP8&c0!*This program uses|
  | Newton,Gs method to find roots of an equation,N|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~V?f0 (Newton)~p0
1 ~V?v0 (k)~p0
1 ~V?v0 ('e)~p0
1 ~V?f0 (f)~p0
1 ~V?f0 (f')~p0
1 ~V?v0 (y)~p0
1 ~V?v0 (x)~p0
1 ~V?c1 ('p)~p0
1 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b$@["! ) # b$@|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW})!# b$@" *|: ;bP8&c0!*Input|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b ]`f#}" *|: ;bP8&c0!*equation|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
1 ~A(f(x)=x^3/2-3*x^2-2*x+6)~p0
255 ~A(f(?x)=1/2*?x^3-3*?x^2-2*?x+6)~p0
2 ~d~sb/_!!   }
b00&!  c#T"_c/__c/__!"}
^ _~A(x=?x)~p0
2 ~d~A(y=f(x))~p0
2 ~d~A(f'(x)=Diff(x)*f(x))~p0
2 ~A(f'(x)=3/2*x^2-6*x-2)~p0
3 ~sb/_!!   }
b00&!  c#T"_c/__c/__!"}
^ _~A(f'(?x)=3/2*?x^2-6*?x-~
 2)~p0
4 ~d~sb/_!!   }
b00&!  c#T"_c/__c/__!"}
^ _~Q
]|Expr|[#b @`bb#_b#_b#_}`f#})## b"0" *|: ;bP8&c0!*convergence|
  | criterion}& b!( b!L b"0 b#8 b%H b&P!WW}]|[~p0
1 ~A('e=10^(-10))~p0
255 ~d~Q
]|Expr|[#b @`bb#_b#_b#_}`f#})## b"0" *|: ;bP8&c0!*maximum iterations|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
1 ~A(k=10)~p0
255 ~d~Q
]|Expr|[#b @`bb#_b#_b#_}`fb#@})!# b%#`f }[#! `fb#@}) # b%#|
  |}# b!( b#8 b$@!WW})%# b%#" *|: ;bP8&c0!*Newton,Gs Method|
  |}# b!( b#8 b$@!WW})5# b%#Newton,Hinitial guess,L "!Symbol^:!&c0  e|
  |: &c0!*,L k,I ,] ,Hroot,L iterations,I|
  |}# b!( b#8 b$@!WW}}}# b!( b#8 b$@!WW}]|[~p1
0 ~A(Newton(?x,?e,?k)=Conditional((?x,k-?k),(abs((f(?x))/(f'(?x)))<~
 ?e)+(?k=0);Newton(?x-(f(?x))/(f'(?x)),?e,?k-1),(1>0)))~p0
1 ~d~A(x_1=Newton(-1,'e,k))~p0
0 ~A(x_1=(-1.5527991074306269,5))~p0
255 ~d~sb/_!!   }
$&!  c#T"!c#L"_c/__c/__}
^ _~A(x_2=Newton(1,'e,~
 k))~p0
0 ~A(x_2=(1.2203843197193109,3))~p0
255 ~d~sb/_!!   }
$&!  c#T"!c#L"_c/__c/__}
^ _~A(x_3=Newton(6,'e,~
 k))~p0
0 ~A(x_3=(6.3324147877622723,4))~p0
255 ~d~sb/_!!   }
$&!  c#T"!c#L"_c/__c/__}
^ _~Q
]|Expr|[#b @`bb#_b#_b#_})!# b"T["! ) # b"T|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW})b I# b"T" *|: ;bP8&c0!*Illustration|
  |                                        |
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~G1 1 230 362
1 1 4 2 10
(-3...8):(-20...20):(?=0...2*'p):('p/~
 5):(10)~Q
]|Expr|[#b @`bb#_b#_b#_}`f#})## b"0" *|: ;bP8&c0!*given function|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~L1 255 ? (x,y):(x=left...right)~p0
1 ~gc0 64 ? 0 -4096 -5837 0
2080 -3836 -3910 0
3120 -3706 -3079 0
5201 -3446 -1665 0
6241 -3316 -1076 0
7411 -3170 -501 0
8321 -3056 -116 0
9362 -2926 261 0
10272 -2812 539 0
11442 -2666 826 0
11848 -2615 909 0
12092 -2584 954 0
12335 -2554 996 0
12646 -2515 1046 0
12921 -2481 1086 0
13653 -2389 1174 0
14221 -2318 1225 0
14563 -2276 1249 0
14953 -2227 1270 0
15603 -2146 1290 0
16952 -1977 1277 0
17226 -1943 1266 0
17684 -1885 1241 0
18724 -1755 1158 0
19455 -1664 1079 0
19894 -1609 1023 0
20235 -1567 976 0
20804 -1495 891 0
22755 -1252 537 0
24965 -975 43 0
27046 -715 -485 0
28086 -585 -763 0
28996 -471 -1011 0
30166 -325 -1333 0
31207 -195 -1617 0
32377 -49 -1932 0
34327 195 -2432 0
35238 309 -2649 0
36408 455 -2909 0
37448 585 -3118 0
38618 731 -3324 0
39529 845 -3460 0
40569 975 -3587 0
41479 1089 -3670 0
42616 1231 -3734 0
43299 1316 -3750 0
44299 1441 -3740 0
44585 1477 -3729 0
44860 1512 -3716 0
45770 1625 -3647 0
46810 1755 -3522 0
47720 1869 -3368 0
48891 2015 -3107 0
49931 2145 -2811 0
51101 2292 -2402 0
52011 2405 -2026 0
53052 2536 -1530 0
53962 2649 -1036 0
55132 2796 -316 0
56172 2926 409 0
57343 3072 1324 0
60203 3429 4031 0
63584 3852 8168 0
65535 4096 11059 0
~
 ~Q
]|Expr|[#b @`bb#_b#_b#_}`fb#@})!# b"0" *|: ;bP8&c0!*roots|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~S17 ? 16711680 ? ? ((x_1)_1,0):(?):(8)~p0
1 ~gc-1 1 ? 0 -3018 0 0
~S17 ? 16711680 ? ? ((x_2)_1,0):(?):(8)~p0
1 ~gc-1 1 ? 0 -953 0 0
~S17 ? 16711680 ? ? ((x_3)_1,0):(?):(8)~p0
1 ~gc-1 1 ? 0 2854 0 0
~Q
]|Expr|[#b @`bb#_b#_b#_})!# b"0" *|: ;bP8&c0!*declarations|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~V?c64 (left)~p0
1 ~V?c65 (right)~p0
1 ~V?c66 (bottom)~p0
1 ~V?c67 (top)~p0
1 ~Q
]|Expr|[#b @`bb#_b#_b#_})%# b"0" *|: ;bP8&c0!*axes and grids|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~X1 0 (x,0):(x=left...right):(x)~p0
1 ~gc1 2 ? 0 -4096 0 0
65535 4096 0 0
~X2 0 (0,y):(y=bottom...top):(~
 y)~p0
1 ~gc1 2 ? 0 -1862 -4096 0
65535 -1862 4096 0
~R11184810 ? (x,y):(~
 y=bottom...top):(x=left...right):(0)~p0
1 ~gc1 2 ? 0 -3351 -4096 0
65535 -3351 4096 0
~gc1 2 ? 0 -1862 -4096 0
65535 -1862 4096 0
~gc1 2 ? 0 -372 -4096 0
65535 -372 4096 0
~gc1 2 ? 0 1117 -4096 0
65535 1117 4096 0
~gc1 2 ? 0 2607 -4096 0
65535 2607 4096 0
~
 ~R11184810 ? (x,y):(x=left...right):(y=bottom...top):(0)~p0
1 ~gc1 2 ? 0 -4096 -2048 0
65535 4096 -2048 0
~gc1 2 ? 0 -4096 0 0
65535 4096 0 0
~gc1 2 ? 0 -4096 2048 0
65535 4096 2048 0
~t~p0
1 ~c2
12 -1 11 -1 13 -1 ~c2
16 -1 15 -1 11 -1 ~c2
17 -1 16 -1 13 -1 ~c11
25 -1 24 -1 19 -1 3 -1 21 -1 2 -1 12 -1 4 -1 17 -1 5 -1 23 -1 1 -1 ~c11
27 -1 26 -1 19 -1 3 -1 21 -1 2 -1 12 -1 4 -1 17 -1 5 -1 23 -1 1 -1 ~c11
29 -1 28 -1 19 -1 3 -1 21 -1 2 -1 12 -1 4 -1 17 -1 5 -1 23 -1 1 -1 ~e