~v200 200 ~w38 0 534 784 0 597 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 1 -1 -1 -1 -1 -1 1 1 ? ? 
~Q
]|Expr|[#b @`bb#_b#_b#_})%# b&P" *|: ;bP8&c0!*Illustrated Newton|
  |,MRaphson}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~V?f144 (RowsOf)~p0
1 ~V?f0 (T)~p0
1 ~V?f0 (Newton)~p0
1 ~V?v0 (k)~p0
1 ~V?v0 ('e)~p0
1 ~V?f0 (f)~p0
1 ~V?f0 (f')~p0
1 ~V?v0 (y)~p0
1 ~V?v0 (x)~p0
1 ~V?c1 ('p)~p0
1 ~Q
]|Expr|[#b @`bb#_b#_b#_})!# b$@["! ) # 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}]|[~p0
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$@ b%H b&P!WW}]|[~p0
1 ~A(k=10)~p0
255 ~d~Q
]|Expr|[#b @`bb#_b#_b#_}`f#})## b"0" *|: ;bP8&c0!*initial guess|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
1 ~A(x_0=0)~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})3# b%#Newton,H$^x^0_,L "!Symbol^:!&c0  e: &c0!*,L|
  | k,I ,] ,Hroot,L iterations,I}# b!( b#8 b$@!WW}}|
  |}# b!( b#8 b$@!WW}]|[~p0
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(x_0,'e,k))~p0
0 ~d~A(x_1=(1.2203843196683553,6))~p0
255 ~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 1 211 554
1 1 4 2 10
(-0.5...3.5):(-14.5...8.5):(?=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$@ b%H b&P!WW}]|[~p1
0 ~L1 255 ? (x,y):(x=left...right)~p0
1 ~gc0 14 ? 0 -4096 3272 0
2080 -3836 3313 0
4030 -3592 3315 0
6241 -3316 3275 0
7411 -3170 3237 0
8321 -3056 3200 0
9362 -2926 3149 0
15603 -2146 2681 0
20804 -1495 2105 0
28996 -471 943 0
51101 2292 -2790 0
56172 2926 -3572 0
60203 3429 -4127 0
65535 4096 -4742 0
~
 ~Q
]|Expr|[#b @`bb#_b#_b#_}`fb#@})!# b"0" *|: ;bP8&c0!*root|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~S17 ? 16711680 ? ? ((x_1)_1,0):(?):(10)~p0
1 ~gc-1 1 ? 0 -573 1069 0
~Q
]|Expr|[#b @`bb#_b#_b#_}`f0})!# b$@" *|: ;bP8&c0!*trace|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~A(T(?x)=((Newton(?x,'e,0))_1,0;(Newton(?x,'e,0))_1,f((Newton(~
 ?x,'e,0))_1);(Newton(?x,'e,1))_1,0;(Newton(?x,'e,1))_1,f((Newton(~
 ?x,'e,1))_1);(Newton(?x,'e,2))_1,0;(Newton(?x,'e,2))_1,f((Newton(~
 ?x,'e,2))_1);(Newton(?x,'e,3))_1,0;(Newton(?x,'e,3))_1,f((Newton(~
 ?x,'e,3))_1);(Newton(?x,'e,4))_1,0;(Newton(?x,'e,4))_1,f((Newton(~
 ?x,'e,4))_1);(Newton(?x,'e,5))_1,0;(Newton(?x,'e,5))_1,f((Newton(~
 ?x,'e,5))_1);(Newton(?x,'e,6))_1,0;(Newton(?x,'e,6))_1,f((Newton(~
 ?x,'e,6))_1);(Newton(?x,'e,7))_1,0))~p0
1 ~d~L3 32768 ? ((T(x_0))_(k_1)):(k_1=1...RowsOf(T(x_0)))~p0
1 ~gc0 9 ? 0 -3072 1069 0
6241 -3072 3206 0
11442 3072 1069 0
15603 3072 -3740 0
20804 -1182 1069 0
24965 -1182 1778 0
30166 -530 1069 0
34327 -530 1016 0
65535 -573 1069 0
~
 ~S1 ? 32768 ? ? ((T(x_0))_(k_1)):(k_1=1...RowsOf(T(x_0))):(4)~p0
1 ~gc-1 15 ? 0 -3072 1069 0
5266 -3072 3206 0
9362 3072 1069 0
14043 3072 -3740 0
18139 -1182 1069 0
23405 -1182 1778 0
28086 -530 1069 0
33352 -530 1016 0
37448 -573 1069 0
42129 -573 1068 0
46225 -573 1069 0
51491 -573 1069 0
56172 -573 1069 0
61438 -573 1069 0
65535 -573 1069 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 1069 0
65535 4096 1069 0
~X2 0 (0,y):(y=bottom...~
 top):(y)~p0
1 ~gc1 2 ? 0 -3072 -4096 0
65535 -3072 4096 0
~R11184810 ? (x,y):(~
 y=bottom...top):(x=left...right):(0)~p0
1 ~gc1 2 ? 0 -3072 -4096 0
65535 -3072 4096 0
~gc1 2 ? 0 -1024 -4096 0
65535 -1024 4096 0
~gc1 2 ? 0 1024 -4096 0
65535 1024 4096 0
~gc1 2 ? 0 3072 -4096 0
65535 3072 4096 0
~
 ~R11184810 ? (x,y):(x=left...right):(y=bottom...top):(0)~p0
1 ~gc1 2 ? 0 -4096 -2493 0
65535 4096 -2493 0
~gc1 2 ? 0 -4096 -712 0
65535 4096 -712 0
~gc1 2 ? 0 -4096 1069 0
65535 4096 1069 0
~gc1 2 ? 0 -4096 2849 0
65535 4096 2849 0
~t~p0
1 ~c2
14 -1 13 -1 15 -1 ~c2
18 -1 17 -1 13 -1 ~c2
19 -1 18 -1 15 -1 ~c13
29 -1 28 -1 25 -1 9 -1 21 -1 5 -1 23 -1 4 -1 14 -1 6 -1 19 -1 7 -1 27 -1 3 -1 ~e