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Quiz1 Solution

The document describes using the bisection method and false position method to find the root of the function f(x) = -25+82x-90x^2+44x^3-8x^4+0.7x^5 on the interval [0.5, 1]. It shows the iterations and results of applying each method, with the bisection method having an error of 10% and the false position method having an error of 2%. It also graphs the function on the interval [0,1.2].

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James Neo
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80 views2 pages

Quiz1 Solution

The document describes using the bisection method and false position method to find the root of the function f(x) = -25+82x-90x^2+44x^3-8x^4+0.7x^5 on the interval [0.5, 1]. It shows the iterations and results of applying each method, with the bisection method having an error of 10% and the false position method having an error of 2%. It also graphs the function on the interval [0,1.2].

Uploaded by

James Neo
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as XLSX, PDF, TXT or read online on Scribd
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b.

) Bisection method
es= 10% xr=(xl+xu)/2
xl= 0.5
xu= 1

iteration xl xu xr f(xl) f(xu) f(xr) es es<10%


1 0.5 1 0.75 -1.478125 3.7 2.072363 33.33333 0
2 0.5 0.75 0.625 -1.478125 2.072363 0.681992 20 0
3 0.5 0.625 0.5625 -1.478125 0.681992 -0.281992 11.11111 0
4 0.5625 0.625 0.59375 -0.281992 0.681992 0.226453 5.263158 1

c.) False Position Method


es= 2%
xl= 0.5
xu= 1

iteration xl xu xr f(xl) f(xu) f(xr) es es<.2%


1 0.5 1 0.642728 -1.478125 3.7 0.918789
2 0.5 0.642728 0.588017 -1.478125 0.918789 0.137289 9.30426 0
3 0.5 0.588017 0.580537 -1.478125 0.137289 0.018219 1.288519 0
4 0.5 0.580537 0.579556 -1.478125 0.018219 0.002378 0.169198 1
f(x)= -25+82x-90x^2+44x^3-8x^4+0.7x^5
a.)Graphically

x f(x)
0 -25 Chart Title
10
0.1 -17.65679
0.2 -11.86058 5

0.3 -7.375099 0
0 0.2 0.4 0.6 0.8 1 1.2
0.4 -3.981632
-5
0.5 -1.478125
0.6 0.321632 -10
0.7 1.588849
-15
0.8 2.480576
0.9 3.140543 -20

1 3.7 -25

-30

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