7. What is the formula of Newton-Raphson method?
Answers
Answer:
The Newton-Raphson method (also known as Newton's method) is a way to quickly find a good approximation for the root of a real-valued function f(x) = 0f(x)=0. It uses the idea that a continuous and differentiable function can be approximated by a straight line tangent to it.
Suppose you need to find the root of a continuous, differentiable function f(x)f(x), and you know the root you are looking for is near the point x = x_0x=x
0
. Then Newton's method tells us that a better approximation for the root is
x_1 = x_0 - \frac{f(x_0)}{f'(x_0)}.
x
1
=x
0
−
f
′
(x
0
)
f(x
0
)
.
This process may be repeated as many times as necessary to get the desired accuracy. In general, for any xx-value x_nx
n
, the next value is given by
x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}.
x
n+1
=x
n
−
f
′
(x
n
)
f(x
n
)
.
Note: the term "near" is used loosely because it does not need a precise definition in this context. However, x_0x
0
should be closer to the root you need than to any other root (if the function has multiple roots).
Explanation:
Answer:
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