Question

Approximate using linearization and compute percentage error:

1/(10.03)^2

Answer 1

let \[f(x)=\frac{ 1 }{ x^2 } , x1=10 , dx=x-x1=.03\]
\[y=y1+f \prime(x1)*dx\]\[y1=\frac{ 1 }{ x1^2 }=\frac{ 1 }{ 10^2 }=.01\]
\[f \prime(x1)=\frac{ -2 }{ x1^3 }=\frac{ -2 }{ 10^3 }=-.002\]\[y=.01-002*.03\]

Answer 2

so \[\frac{ 1 }{ 10.03^2 }=.01-.0006=.0094\]

Answer 3

Hey, you are the man. Thank you so much!

Answer 4

you are so welcome :) , and I am sorry if I got any wrong in these calculations

Answer 5

hold on, when you say x1, would that also mean f(a)? my professor seems to use different terms than everyone else

Answer 6

No worries, the concept was my only concern, I can double check the calculations. Thanks!

Answer 7

no no yuor prof is right x1,a, they are just numbers we choose to simplify the calculations

Answer 8

Ok cool. Also, do you know how to find percentage error?

Answer 9

you can say that ;)

Answer 10

Haha how would you go about doing that?

Answer 11

I would be so happy to do that

Answer 12

I don't know how to find the percentage error

Answer 13

ohh is that the last part on there?

Answer 14

Haha my bad I got it all mixed up but I get it!

Answer 15

okay, the percentage error is esimated with this rule:\[\frac{ f \prime (x) }{ f(x) }*100\]

Answer 16

Cool, cool. Sorry got confused haha. Thanks for clearing that up

Answer 17

okay but notice that I said esimated , and that what usually we need

Answer 18

yup, it says to estimate for me so i think that will do it

Answer 19

okay good luck and if you needed anything I will be around ;)

Answer 20

You're a life saver right now

Answer 21

Sorry I actually don't get why you had to do that last step. the .01-.0006

Answer 22

Like I understand the math, but don't understand why you had to do it

Answer 23

NEVERMIND IGNORE THAT! Brain fart

Answer 24

I did nothing dude just substitution in the original equation which is \[y=y1+f \prime(x1) dx\]

Answer 25

lol no no I liked that fart actually

Answer 26

Lol the worst kind of fart

Answer 27

okay there three things in mind right now:
the first did you understand why we did the last step?
second: is it safe to use that idiom ( brain fart) I kinda liked it lol
the third: I have to admit, you are the coolest guy in this entire site ;)

Answer 28

Hahah thanks bud! This was my first time using the site, so so far you have been my favorite! Yes I completely understand it now though, like I said my prof uses different terms so I just had to translate that, but then it was smooth. Lol hey whatever kinda farts you're into! I always get a kick out of brain fart :)

Answer 29

Got to go take my test now that I'm feeling more confident about it. Thanks much for the help!

Answer 30

lol , okay I wish you very good luck in your exam, just whenever you got stuck in a question, remember that question is nothing but a prof brain fart :)