find the cube root of 12 upto decimal place by Newton-Raphson's methhod .
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Answer:
12
Let x=
12
x
2
=12
x
2
−12=0
Iterative eqn. for Newton-Raphson method is
x
n+1
=x
n
−
f′(x
n
)
f(x
n
)
Substitute f(x)=x
2
−12
∴ x
n+1
=x
n
−
2x
n
(x
n
2
−12)
First iteration :-
x
1
=x
0
−
2x
0
(x
0
2
−12)
x
0
is a no. closer to
12
9
<
12
<
16
∴ x
0
=3.5
x
1
=3.5−
2∗3.5
[(3.5)
2
−12]
x
1
=3.5−0.0357
x
1
=3.4643
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