Three Methods to Find Roots of Equations
There are many different kind of methods which can be used to find the
roots of equations which can not be sold algebraically. In this
coursework we are going to analyse the use of three of these methods
which are called the: change of sign, Newton-Raphson and the
rearrangement method and are going to use them to find roots of
different equations.
Change of sign method
A root of an equation (where the graph crosses the x-axis) can be
detected by finding where the solution of a formula changes sign from
positive to negative. Where we find a change of sign on a graph using
omnigraph we take the range of the numbers it is in and divide it by
ten to find where it now changes sign. This procedure is then repeated
to the required level of accuracy.
Here is a graphical representation of the systematic decimal search:
[IMAGE]
X 1
X 10-1
X10-2
Using change of sign method on excel
First you look up between 2 values (e.g. 1 and 2, or 4 and 5) where
the graph crosses the x-axis. Then you take that as your range and
divide it up into 10 equal segments. For example, if between 1 and 2..
you use 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, etc. you work out the formula
for each of these and where the change of sign occurs you repeat the
process between that range.
A
B
C
D
E
E
1
X1
f(A1)
A2+0.01
f(C1)
C1+0.001
f(C1)
2
A1+0.1
f(A2)
C1+0.01
f(C2)
E1+0.001
f(C2)
3
A2+0.1
f(A3)
C2+0.01
f(C3)
E2+0.001
f(C3)
4
A3+0.1
f(A4)
C3+0.01
f(C4)
E3+0.001
f(C4)
5
You solve this problem by plugging in 2, 3, 4, 5, and 6 for x.
Addition and Subtraction- in that order as well. To explain this, we will solve the problem above:
order to do this you really need to try to put together an explanation of
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easier it is to plot a graph and draw in the line of beat fit. I
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S.D = ? (1141.5 – 1122.30)2 + (1115.06 – 1122.30)2 + (1110.35 – 1122.30)2 / 3-1
Below is a list of all the variables I can consider to use in my
every number. Then move your ruler down to the bottom. No, put it across the bottom. Now
The next step was to graph the results. I was able to do this very
The era of the American Revolution was a time of great nationalism, hope, and unity. People who were once only colonists were now citizens of a new and exciting nation. As the years wore on, however, the citizens of the United States were faced with the reality of building a country. The nation strove to find a place for itself, to become secure against the power of the rest of the world. Industry grew along with the population, but what the new country gained in strength it lost in spirit. Regional tensions emerged as well as burning political issues. In the aftermath of the civil war the still young nation attempted to regain this nationalism that was once the strength of the country. One area this attempt was prominent in was literature. Two poets specifically sought to find a national mythology by examining what American's value and why it is necessary to pass it on through tradition. The poems by John Greenleaf Whittier and Henry Wadsworth Longfellow are a call for preserving the roots found in the land of America and in the heart of an American.
I then put these results into a graph which you can find in the plastic wallet this was handed in with.
a calculator, plug the function into the y= button. Next click on the graph button and view your