Gain Immediate access to our Essays
FREE access exchanged for your work, or pay £4.99
Your Status: Logged out
Student Central helps you learn fast, by providing unlimited access to 117,981 essays and coursework documents written by GCSE & A Level students.
Register for FREE now by publishing your essays, or pay as little as £4.99 per month.
Essays in Core & Pure Mathematics category
-
Solution of equations by numerical methods.
... for equation solution. This comparison will also include the negative and positive points of each method, such as problems that result in an inability to find the correct root and the speed of convergence to the correct root. Fixed Point ...
-
Solutions of equations
... graph of this function is given below. I then decided to confirm the shape of the graph by finding how many turning points there is. Dy = 729x2-756x+192 = 0 Dx Quadratic Equation: D= b2-4ac =-7562-(4*729*192) =11664> 0 => 2 Real Turning Points (Graph Shape Confirmed) By ...
-
Solutions of Equations by Numerical Methods - Change of sign Method and Decimal Search Method.
... the interval [-1, 0] f(-1) = -1-2+3-1/2 = -1/2 f( 0 ) = 0-0-0-1/2 = -1/2 The function f(x) is continuous therefore to show that there is a real root a change in sign should occur. However this is the failure of the ...
-
Solve the equation: X3- 5X-5 = 0. This equation cannot be factorised nor solved algebraically therefore it must be solved through interval bisection.
... 0.0005. Therefore it can be said that that 2.627
- Solving Cubic equations or polynomials of greater order
... factors include decimal places this can be difficult. So I lastly tried to solve the equation using graphs, this was extremely hard as the cubic graph needs more detail and I found that the graph as before was only correct ...- Solving equations by numerical methods - The Interval Bisection method
... interval limits. The error bunds are a and b, so that x is between the two values. The error bounds for this root of the equation x³+2x²-x-3=0 are 1.1474609375- Solving Equations by numerical methods.
... are not. A comparison between the methods will also be attempted. Method 1: Decimal Search SOLVING AN EQUATION WITH THIS METHOD Fig1. Shows the function f(x) = 12 ln(x) - x3/2. (Where ln(x) represents the natural logarithm of x.) To find the roots, the ...- Solving Equations Numerically
... a interval with a root in it, f(x) will change sign. For example, in the diagram to the left, we know that there is a root between 1 and 2. Decimal Search There are three good ways of getting as close to the ...- Solving Equations using Numerical Methods.
... - f (xn) f ` (xn) xn+1 = xn - (xn5 - 4xn+1) (5xn4 -4) When x1= 0 x2 = 0 - ((0)5 - 4(0) + 1) 5 (0)4 - 4 = 0 - 1 -4 = ...- Solving the equation of 0 = 3x^5 - 3x + 1 using different methods
... the Newton Raphson method as it took the least iterations/calculations. However, all three methods do have their strengths and weaknesses. The Decimal Search/Change of Sign can not calculate the value of the function if the curve is a tangent ...- Systematic search for a change of sign - pure maths
... only need to calculate values until there is a change of sign, one need not go further. These are the limits for the root, which must lie between them. We can find the next decimal value of the root by ...- Testing Root Methods
... roots in between two integer values. Method 2: Newton-Raphson Method Using Autograph again, the roots for y=x5 -3x2 + 1 were found using the Newton-Raphson Method: This illustration demonstrates how we acquire the first root of the equation. The tangent is found at ...- The aim of this coursework is to compare three different numerical methods of solving equations. This will allow us to determine which one is the most efficient, quickest and easiest method to use.
... of accuracy. The equation that I have chosen to solve is x5 - 2.7x + 1.8 = 0 The graph illustrates y = x5 - 2.7x + 1.8 Zoom of y = x5 - 2.7x + 1.8 between x = -2 and x ...- The Change of Sign method locates the root of an equation by where it crosses the x-axis.
... find the interval of the change of sign with greater accuracy. x y 1.1 -0.205 1.11 -0.00344 1.12 0.20224 1.13 0.412085 The table shows a change of sign between 1.11 and 1.12. The root is in the interval [1.11,1.12] x y 1.1 -0.0034 1.111 0.016937 1.112 0.037361 1.113 0.05782 This table now shows that the root is in the interval [1.11,1.111]. Error Bounds X= Failure ...- The diagram shows a house built with dominoes. This house has four stories and uses 24 dominoes.Simon broke the World Record by building a domino house with 73 stories. How many dominoes did he use?
... a results table where I will comment on why I am using the results and what purpose it has in my project. I will also explain if I can spot any patterns. After I spot the patterns I will work ...- The open box problem
... and see if I can find any patterns. If so, then I will be able to come up with a hypothesis, which I can then test to see if I can solve this first objective. Then I will attempt to ...- The Rational Zeros
... smallest positive root, expressed as a fraction is The same principle as that seen before is observed in this curve which has fractional coefficients: the denominator is equal to the first coefficient and the numerator is equal to 1 as ...- There are three snails; slippery, slimy and slidey. They enter a ten-metre race for food. Each snail runs according to the following rules. Slippery : d= 4.4 + 0.55t Slimy : d= 0.3t(t-7) Slidey : d= 0.3t(t-3.4)(t-9)
... 0.3(0)(0-3.4)(0-9) = 0(-3.4)(-9) = 0(m) Name of snails Slippery Slimy Slidey Distance (m) 4.4 0 0 (A distance of each snail when the time is 0 min.) (b) 2minutes Slippery : d = 4.4 + 0.55t = 4.4 + 0.55(2) = 4.4 + 1.1 = 5.5(m) Slimy ...- Three ways of reading The Bloody Chamber.
... the signifier, the first tem in the semiology of myth, is already an item which is full of meaning, a sign. The following diagram should help to clarify Barthes point. signifier signified sign SIGNIFIER SIGNIFIED SIGN Here, the first order ...- Transformation of Quadratic Functions.
... x2 +1 y = x2 - 4 y = 5 - x2 What does the graph show you about the effect of "C" on the shape and orientation of the graph of y = Cx2 , C>0? y = 3x2 y = 1/2 x2 Overall ...- Triminoes Investigation
... double the previous value. In the example of exponential growth the next term is obtained by multiplying the previous term by 1.5. Powers of two 1, 2, 4, 8, 16, ... Exponential growth 10, 15, 22.5, 33.75, ... Exponential decay 20, 16, 12.8, 10.24, ...- Using a Spreadsheet to Analyse Statistics
... Access. 3. Sorting the Data You notice that the teams are not listed in alphabetical order and you decide that you want to put this right. 1. You must first select columns B and C It is very important that you do this. ...- Using Decimal search
... me that 10x^3-2.5x+0.2=0 has three roots, lying in the intervals (-1,0), (0,1). X -1 0 1 Y -7.3 0.2 7.7 I can stop here as there is no change of sign in interval (0,1). Even though no root is indicated, the graph shows 2 roots which this method ... - Solving Cubic equations or polynomials of greater order