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    can someone help me answer these questions? I've tried but I still can't find an answer!!!
    The three methods the questions are referring to are: rearrangement method g(x), Newton-Raphson iteration and change of sign decimal search

    1. here is the graph of a function (x)=(x^3-3x+10)^1/2. What problems, if any, would you expect when using any of the three methods to find the root?
    2. What problems would you expect when using any of the three methods when trying to find the root in [0,1] of f(x)=In (cos(sin (x))-sin(cos(In x))?
    3. How did you find suitable functions that you used for your graphs?
    4.f(x)= x-cos(x). Which method would you use to find the root of this function?

    Thank you
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    (Original post by esmeralda123)
    can someone help me answer these questions? I've tried but I still can't find an answer!!!
    The three methods the questions are referring to are: rearrangement method g(x), Newton-Raphson iteration and change of sign decimal search

    1. here is the graph of a function (x)=(x^3-3x+10)^1/2. What problems, if any, would you expect when using any of the three methods to find the root?
    2. What problems would you expect when using any of the three methods when trying to find the root in [0,1] of f(x)=In (cos(sin (x))-sin(cos(In x))?
    3. How did you find suitable functions that you used for your graphs?
    4.f(x)= x-cos(x). Which method would you use to find the root of this function?

    Thank you
    1. Well first of all, for Newton-Raphson, what would happen if while you approximate the root you run into the scenario where x_i=\pm 1?? Look at the formula for it and see where the trouble lies. Then for change of sign, we know that for one side of the root the function takes a positive value, and for the other side it takes the negative value. But do we have the function on both sides of the root?

    2. With newton Raphson, same problem as above. With change of sign, I don't know whether this is a problem depending what you use, but you should notice that the distance between the roots gets smaller and smaller as x\rightarrow 0 so at some point they so would be so close together that it would become hard to approximate a specific one. With rearrangement, does your starting point affect which root you'll approximate?

    3. Dunno what this question is supposed to mean

    4. Observe its graph, which method wouldn't cause you any problems?
 
 
 
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