Using newton Raphson method find the approximate value of 3√100
Answers
Step-by-step explanation:
To find an approximate value for c:
Start with an initial approximation x0 close to c.
Determine the next approximation by the formula x1=x0−f(x0)f′(x0).
Continue the iterative process using the formula xn+1=xn−f(xn)f′(xn) until the root is found to the desired accuracy.
Answer:
4.646
Step-by-step explanation:
Concept= Newton Raphson Method
Given= 3√100
To Find= approximate value of 3√100
Explanation=
Newton Raphson Method is used to find the approximate value of the given function. It is the geometric interpretation of the function.
The formula of Newton Raphson Method is
yₙ₊₁= 1/b[(b-1)yₙ + a/yₙᵇ⁻¹]
so in 3√100 the value of a=100 and b=3
Let the approximate value of 3√100 be 4.5
Therefore y₀=4.5
We do this for now n=0
y₁= 1/3[(3-1)y₀ + 100/y₀²]
=> 1/3[2y₀ +100/y₀²]
=> 1/3[2*4.5 + 100/4.5²]
=>1/3[ 9+4.938]
=>1/3[13.938]
=>4.646
y₁= 4.646
Therefore the approximate value of 3√100 is 4.646.
According to Newton Raphson Method the value of 3√100 is 4.646
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