3. Newton’s iterative formula for finding the square
root of a positive number N is x
n+1
= _______.
Ans:
1
()
2
nn
xNx
⎞
−
⎠
4. Newton’s iterative formula for finding the recip-
rocal of a number x
n+1
= _______.
Ans:x
n
(2 −Nx
n
)
5. Newton iterative formula for finding the pth
root of a positive number N is x
n+1
= _______.
Ans:
1
1
(1)()
p
nn
pxNx
p
−
⎡⎤
−+
⎣⎦
6. Newton’s iterative formula for finding the cube
root of a number N is x
n+1
= _______.
Ans:
2
1
2
3
n
n
N
x
x
⎡⎤
+
⎢⎥
⎣⎦
7. The cube root of 24 by Newton’s formula, taking
x
0
= 3 is _______. Ans: 2.889
8. The square root of 35 by Newton’s formula
taking x
0
= 6 is _______. ...
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