Question

Not really sure how to write the first four terms. I'm guessing f, f',f",f"'. Use known series to expand sqrt(a+R) in terms of R/a when |R| is much smaller than a. Display the first 4 non-zero terms.

Answer 1

\[\sqrt{a+R}\rightarrow \sqrt{a}\sqrt{1+\frac{R}{a}}\]

Answer 2

derivative i guess
what is the variable? \(a\)? what are you expanding about?

Answer 3

you got some goofy questions tonight for sure

Answer 4

Honestly no idea. Yeah my professor thinks this is good practice for our exam tomorrow.

Answer 5

actually now that i read the question, probably not successive derivatives
it says "use known expansion"

Answer 6

oh so taylor series then...

Answer 7

so like the series for (1+x)^k

Answer 8

maybe \[\sqrt{1+x}\] if \(R\) is much smaller than \(x\) this is expanding about 0
maybe someone else has a better idea

Answer 9

yeah like that, for \(k=\frac{1}{2}\)

Answer 10

but what about sqrt(a) do I just kind of bring it along for the ride or?

Answer 11

maybe take the expansion for \[\sqrt{1+x}\] replace \(x\) by \(\frac{R}{a}\) then multiply by \(\sqrt{a}\)

Answer 12

like i said (maybe)

Answer 13

alright I'll see if that works out

Answer 14

lol good luck!