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use Newton-Raphson Method to find root

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I need some help on the Newton-Raphson method. The question goes as follows:

The velocity, v mm/sec. of a point on an eccentric cam at a certain instant is given by V= 0.3 x-ln x, where x is the displacement in mm.

1 a) Show that when the velocity is zero the displacement lies between 1 and 2 mm.
b) Use the Newton-Raphson method to determine this displacement for the velocity to be zero. Give your answer to 4 significant figures.

2 a) By drawing a suitable graph, or graphs, show that x = 2sin²x has one solution in the region of x=0.5.
b) Find this root correct to 4 significant figures by using the Newton-Raphson method.

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The solution provides detailed explanation how to use Newton-Raphson Method to find roots.

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