Fluent Essays

check all the files and tell me can you do itWhatsApp Image 2021-02-21 at 12.59.26 AM.jpeg 5903312.pdf Bisection Method Steps for employing Bisection Method: Theorem An equation 0)( xf , where )(xf is a real continuous function, has at least one root between x and u x if 0)()(  u xfxf  (See Figure 1). Note that if 0)()(  u xfxf  , there may or may not be any root between x and ux (Figures 2 and 3). If 0)()(  u xfxf  , then there may be more than one root between x and ux (Figure 4). So the theorem only guarantees one root between x and ux . Bisection method Bisection Method Since the method is based on finding the root between two points, the method falls under the category of bracketing methods. Since the root is bracketed between two points, x and ux , one can find the mid-point, mx between x and ux . This gives us two new intervals 1. x and mx , and 2. m x and u x . Figure 1 At least one root exists between the two points if the function is real, continuous, and changes sign. f (x) xℓ xu x f (x) xℓ xu x Bisection Method Figure 2 If the function )(xf does not change sign between the two points, roots of the equation 0)( xf may still exist between the two points. 5903337.pdf Finishing off the report: 1. when you have finished your coursework, you should read it through carefully to make sure that you have included everything required and that it is all done correctly. You may find it helps to print it out to do this. 2. Make sure you have numbered the pages! 3. Read through carefully for typos and to make sure that what you have written makes sense and things are in the correct order. It’s easy to muddle things up when cutting and pasting a lot. Make sure all the formulae have printed out correctly. 4. Make sure you have stated the equation in the form …… = 0 that you are trying to find a root of, for every method (including in the failure cases)and again in the comparison. 5. You may refer to your function, e.g. f(x) = x3 – 3x + 1 but make sure you don’t call that an equation! 6. Make sure that all your graphs are fully annotated: i. Axes should be labelled. ii. Curves should be labelled. (y = f(x) is fine provided it is clear in the text what your f(x) is.) iii. Positions of x0 to at least x2 should usually be labelled. (It may only be possible to show x0 and x1 in the failure of g(x).) iv. Tangents should be labelled. 7. You should have explained how each method works. 8. All roots found should be stated clearly: x = … with a maximum error of ±0.000005. For the iterative methods, the x value has 5 d.p. but for decimal search it has 6 digits after the decimal point, the last of which is a 5 (because you took a midpoint). 9. Make sure you have used correct subscripts on all the x’s in your iterative formulae. 10. Make sure that you marked your own work following the marking criteria guidelines. WhatsApp Video 2021-02-27 at 7.54.39 PM.mp4 WhatsApp Video 2021-02-27 at 7.54.39 PM (1).mp4 WhatsApp Video 2021-02-27 at 7.54.39 PM (2).mp4 WhatsApp Video 2021-02-27 at 7.54.39 PM (3).mp4 WhatsApp Video 2021-02-27 at 7.54.39 PM (4).mp4