Question

Does anybody here know much about Perturbation Theory? I'm reading a book on it and am running into some issues. Also need some help with some plain old Calculus limits shown in the book that are confusing me.

Answer 1

https://dl-web.dropbox.com/get/Screenshot_2014-12-14-01-35-38.png?_subject_uid=221661082&w=AABKsPWkjHhWUQobavEZz6VZvgNxJIZR2SAypN4f8DYwDQ

Answer 2

\[z_{1}(\epsilon)=\lim_{\epsilon \rightarrow 0}\frac{1-\sqrt{1-\epsilon}}{\epsilon}=2z-1\]

Answer 3

\[z_{2}(\epsilon)=\lim_{\epsilon \rightarrow 0}\frac{1+\sqrt{1-\epsilon}}{\epsilon}=\infty\]

Answer 4

(I also don't honestly remember from limits how to mathematically verify that last one, either. Going to Wolfram|Alpha to poke around as well.)

Answer 5

Wolfram|Alpha gets something different, too; am I misreading the book? http://www.wolframalpha.com/input/?i=limit+as+epsilon+approaches+0+of+%281-sqrt%281-epsilon%29%29%2Fepsilon

Answer 6

*

Answer 7

What? But yeah, it's this part precisely right here that I don't get, math-wise. http://i.imgur.com/aSQN5rl.png

Answer 8

Page before: https://dl-web.dropbox.com/get/Screenshot_2014-12-14-01-50-15.png?_subject_uid=221661082&w=AAAUi8fwe19Xz-jrgMxgnDhVFMM4_1u4BpFfuI-5E_Fluw

Answer 9

"The first quantitative step" is the beginning of the relevant section.

Answer 10

Hey, in that sentences where it says, "If epsilon equals zero, z_{1}(epsilon)=1/2", that's the exact same answer W|A got when taking the formal limit; so the other things aren't formal limits, or what?

Answer 11

I have no idea what the heck is going on in this book; this is literally the first few pages and there hasn't been any crazy math, and then this shows up and it just appears to not make any sense.

Answer 12

@tkhunny

Answer 13

#1 If it says \(\epsilon = 0\), it has nothing to do with a limit.

Have you considered "rationalizing" your numerator?

Answer 14

Read the part beneath that where it declares epsilon zero, where it says "as epsilon approaches" and gives one of the results as infinity; that must be Calculus, or something else.

Answer 15

@tkhunny Right arrow, not equals sign. http://i.imgur.com/aSQN5rl.png

Answer 16

That makes a lot more sense. Now, how about the rationalizing?