MHT CET · Maths · Application of Derivatives
The positive root of \(x^{2}-78.8=0\) after first approximation by Newton Raphson method assuming initial approximation to the root is 14, is
- A \(9.821\)
- B \(9.814\)
- C \(9.715\)
- D \(9.915\)
Answer & Solution
Correct Answer
(B) \(9.814\)
Step-by-step Solution
Detailed explanation
Here, \(\quad x_{0}=14, f(x)=x^{2}-78.8\)
and \(f^{\prime}(x)=2 x\)
\(\therefore x_{1}=x_{0}-\frac{f\left(x_{0}\right)}{f^{\prime}\left(x_{0}\right)} \)
\(=14-\frac{(14)^{2}-(78.8)}{2 \times 14}=9.814\)
and \(f^{\prime}(x)=2 x\)
\(\therefore x_{1}=x_{0}-\frac{f\left(x_{0}\right)}{f^{\prime}\left(x_{0}\right)} \)
\(=14-\frac{(14)^{2}-(78.8)}{2 \times 14}=9.814\)
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