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The approximate value of a root of x3 – 13 = 0, then 3.5 as initial value, after one iteration using Newton-Raphson method, is 
  • a)
    2.687
  • b)
    2.678
  • c)
    3.607
  • d)
    3.597
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The approximate value of a root of x3 – 13 = 0, then 3.5 as init...
Concept:
Newton-Raphson Method:
The iteration formula is given by

Where x0 is the initial value/root of the equation f(x) = 0
Calculation:
Given:
f(x) = x3 - 13, x0 = 3.5
f'(x) = 3x2
f(x0) = f(3.5) = 3.53 - 13 = 29.875
f'(x0) = f'(3.5) = 3 × 3.52 = 36.75
We know that

∴ x1 = 2.6871
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Community Answer
The approximate value of a root of x3 – 13 = 0, then 3.5 as init...
The value of a root of x^3 can vary depending on the specific equation or context. Without more information, it is not possible to determine an approximate value.
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The approximate value of a root of x3 – 13 = 0, then 3.5 as initial value, after one iteration using Newton-Raphson method, isa)2.687b)2.678c)3.607d)3.597Correct answer is option 'A'. Can you explain this answer?
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