show that the iterative formula
for finding the recriprocal of N
is xn+1- xn (2-Nxn) and hence
find
the value of
1÷31 upto 4
decimal places.
Answers
Answered by
1
Answer:
Let x=
3
N
⟹x
3
=N
⟹x
3
−N=0.
Newton-Raphson method ⇒ x
n+1
=x
n
−
f
′
(x
n
)
f(x
n
)
f(x)=x
3
−N
f
′
(x)=3x
2
∴ x
n+1
=x
n
−
3x
n
2
x
n
3
−N
x
n+1
=x
n
−
3x
n
2
x
n
3
+
3x
n
2
N
x
n+1
=x
n
−
3
x
n
+
3x
n
2
N
x
n+1
=
3
2x
n
+
3x
n
2
N
x
n+1
=
3
1
[2x
n
+
x
n
2
N
]
Answered by
0
Answer:
hdgdghddgjnexgdddjfkker
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