# Homework 5

## Homework 5

I'll go ahead and get this started by saying "Lesson Learned."

Just go ahead and write a script file to do your calculations for you. Problem 7.9a takes 23 iterations, and each iteration took me half an hour to calculate by hand (I completed six). FML

Just go ahead and write a script file to do your calculations for you. Problem 7.9a takes 23 iterations, and each iteration took me half an hour to calculate by hand (I completed six). FML

**Melissa**- Posts : 12

Join date : 2011-11-01

Age : 39

Location : Euless

## Re: Homework 5

For anyone needing a last minute reminder, even though the only members so far are two people other than me who have already finished the homework, the problem numbers are:

Ch 6: 1,5,19,21,24

Ch 7: 9

Ch 6: 1,5,19,21,24

Ch 7: 9

## Re: Homework 5

Melissa wrote:each iteration took me half an hour to calculate by hand (I completed six). FML

jk. Sounds miserable.

## Re: Homework 5

6.1: I got 9 iterations with a root of 0.7686

Used the equations:

x(i+1) = sin[sqrt[x(i)]]

ea = abs[[x(i+1)-x(i)]/x(i+1)] x 100%

6.5: a) I got 6 iterations with a root of 6.4747

Used the equations:

f(x) = x^5 - 16.05x^4 + 88.75x^3 - 192.0375x^2 + 116.35x + 35.6875

f ' (x) = 5x^4 - 64.2x^3 + 266.25x^2 - 384.075x + 116.35

x(i+1) = x(i) - f[x(i)] / f ' [x(i)]

ea = abs[[x(i+1)-x(i)]/x(i+1)] x 100%

b) I got 7 iterations with a root of 5.0814

Used the equations:

f(x) = x^5 - 16.05x^4 + 88.75x^3 - 192.0375x^2 + 116.35x + 35.6875

f(x+dx) = (x+dx)^5 - 16.05(x+dx)^4 + 88.75(x+dx)^3 - 192.0375(x+dx) + 116.35(x+dx) + 35.6875

x(i+1) = x(i) - dx(i)*f[x(i)] / [f[x(i)+dx(i)]-f[x(i)]]

ea = abs[[x(i+1)-x(i)]/x(i+1)] x 100%

6.19: when w(0) = 1, w = -220.0202

when w(o) = 1000, w = 220.0202

6.21: theta = 0.6625 radians or 37.9590 degrees

6.24: numerator factors to (s+4)(s+3)(s+2)

denominator factors to (s+6)(s+5)(s+3)(s+1)

(s+3) can be eliminated from numerator and denominator

7.9: a) Took 23 iterations with a root at -0.347259424198835

Used the equations:

f(x)= x^4+2x^3+8x^2+5x

ea=(2-ϕ)|(xu-xl)/x_opt |×100%

d=(ϕ-1)(xu-xl)

x1=xl+d

x2=xu-d

b) about to work on right now

Used the equations:

x(i+1) = sin[sqrt[x(i)]]

ea = abs[[x(i+1)-x(i)]/x(i+1)] x 100%

6.5: a) I got 6 iterations with a root of 6.4747

Used the equations:

f(x) = x^5 - 16.05x^4 + 88.75x^3 - 192.0375x^2 + 116.35x + 35.6875

f ' (x) = 5x^4 - 64.2x^3 + 266.25x^2 - 384.075x + 116.35

x(i+1) = x(i) - f[x(i)] / f ' [x(i)]

ea = abs[[x(i+1)-x(i)]/x(i+1)] x 100%

b) I got 7 iterations with a root of 5.0814

Used the equations:

f(x) = x^5 - 16.05x^4 + 88.75x^3 - 192.0375x^2 + 116.35x + 35.6875

f(x+dx) = (x+dx)^5 - 16.05(x+dx)^4 + 88.75(x+dx)^3 - 192.0375(x+dx) + 116.35(x+dx) + 35.6875

x(i+1) = x(i) - dx(i)*f[x(i)] / [f[x(i)+dx(i)]-f[x(i)]]

ea = abs[[x(i+1)-x(i)]/x(i+1)] x 100%

6.19: when w(0) = 1, w = -220.0202

when w(o) = 1000, w = 220.0202

6.21: theta = 0.6625 radians or 37.9590 degrees

6.24: numerator factors to (s+4)(s+3)(s+2)

denominator factors to (s+6)(s+5)(s+3)(s+1)

(s+3) can be eliminated from numerator and denominator

7.9: a) Took 23 iterations with a root at -0.347259424198835

Used the equations:

f(x)= x^4+2x^3+8x^2+5x

ea=(2-ϕ)|(xu-xl)/x_opt |×100%

d=(ϕ-1)(xu-xl)

x1=xl+d

x2=xu-d

b) about to work on right now

**Melissa**- Posts : 12

Join date : 2011-11-01

Age : 39

Location : Euless

## Re: Homework 5

Melissa wrote:6.5: a) I got 6 iterations

How?? I just ran it in matlab and it runs like 22 iterations...? x(i+1) is 2.3 something at first, and then jumps way up to 90 something, and then starts shrinking down slowly. So while matlab ran all the calculations super fast, I really don't wanna write down 22 iterations lol.

## Re: Homework 5

Maybe I did it wrong, because George described something like that also. If you get to class early we can compare.

**Melissa**- Posts : 12

Join date : 2011-11-01

Age : 39

Location : Euless

## Re: Homework 5

I've surrendered and aligned with George's philosophy pretty much this time around since I'm out of time. Matlab ftw! I can do the work. I just know the repetition is going to take too damn long. Done by hand, these problems really are meant to be done bout one a day--not all at once.

EE@UTA...and...yeah. :: EE Help :: EE 2347: Mathematical Foundations (Computer Methods) of EE (MATLAB)

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