Good point. I also believe I found a bound. it's a nasty number but it's off the assumption that |z-i|< δ< .5
I attached the pdf. I think I'm getting better with inequalities. Thanks so much for your help thus far!
Sorry the last bit was meant to say
∴ \lim_{z \rightarrow i} \frac{z^2 + i}{z^4 -1} = ∞
not:
∴ \lim_{z \rightarrow i} \frac{z^2 + i}{z^4 -i} = ∞
Does this fix that issue? Because now I don't see the division by zero issue.
I wasn't 100% sure of how proving that limit equals zero would help but I did take your advice and broke the problem into several limits whose products are infinity.
I used the idea of bounding |z+i| by 3 by assuming delta was at most 1. I attached a pdf of my work. If someone could check it...
In the picture to the left they're summing up the potential energies but I don't understand why they equal to (Q^2)/2C. Almost like both of them put together is like a giant capacitor? Not sure how they got this any help would be appreciated. This is coming from the book University Physics 13e...
I'm reading University Physics 13e by Young and Freedman and we're given this equation:
-L(di/dt)-q/C=0
So we know that i, current, is, i=dq/dt. So the first equation can be read, after some simplification, as
q''+(1/LC)q=0
where q prime means the derivative of q (charge) with...
Not sure if anyone noticed this. But if you're in word/onenote 2007 or 2010 if you go to File (or that big random windows symbol in the upper left corner in 2007), then options, revision, and then click Autocorrection Options. There is a tab for math autocorrection. Here you can see all the...
Another thing I've noticed. When you paste the equation editor text into a, let's say a web browser search. For instance I made the nth root of 2x, but when I paste it here it looks like:
√(n&2x). Meaning that the shortcut is \sqrt (n&2x), luckily that works! So doing this may reveal other...
One thing I wanted to add to this that I found in another thread was how to do custom matrices: the syntax is:
\matrix (a1@b1@c1@...&a2@b2@c2&...)
where the "@" symbols separate different column elements, and ampersand "&" separate different row elements after typing "\matrix" you see a black...