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Q.5. Using Newton Raphson method find the cube root of 41 correct to three decimal place. |
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Answer» Answer: To find the cube root of 24 USING Newton - Raphson method, we need to SOLVE f(x)=x³−24. ⇒f′(x)=3x²
Notice 3³=27 Therefore the cube root of 24 is slightly LESS than 3. We have f(x)=x³−24,f'(x)=3x²
Let us start ESTIMATING the root x Let the first estimation be a=2.9 (slightly less than 3) Hence the subsequent estimates will be b=a− f′(a)/f(a) ,c=b−f′(b)/f(b). f(a)=f(2.9)=(2.9)³−24=0.389 and f'(a)=f′(2.9)=3(2.9)²=25.23 Therefore b=2.9− 25.23/0.389 ≈2.88458 Now c=2.88458− f ′(2.88458)/f(2.88458)
=2.88449 Hence the cube root of 24 is 2.884. ☺️☺️ |
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