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# Newton raphson method

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For a i applied the newton raphson method which is $$x=1+\frac{sin1 +2(1)-3}{cos1 + 2}$$ which gave me value of 0.938(3sf) i assume this is correct

Nov 23, 2019

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Sorry, but your assumption is not correct.

There are two mistakes in your application of the Newton-Raphson formula.

The formula is

$$\displaystyle x_{n+1}=x_{n}-\frac{f(x_{n})}{f'(x_{n})}.$$

The sign in front of the second term on the rhs is a negative.

The other mistake is in the differentiation of f(x), the term xsin(x) should be differentiated as a product,

there should be three terms on the bottom line of that fraction.

The second part of the question is asking you if you understand the basis of the method, and that sometimes it doesn't work.

Draw the tangent to curve at x = 5, the second approximation will be the value of x where this crosses the x-axis, somewhere just above x = 4.

Repeat the process, the next approximation will be where the tangent to the curve for this value of x crosses the x-axis, somewhere close to x = 5.

Repeating the process just gets you an oscillation about the minimum point of the curve, you never get down to the root close to x = 1.

Nov 24, 2019