9—Vector Calculus 1 2829.47 Fill in the missing steps in deriving Eq. ( 45 ).
9.48 Analyze the behavior of Eq. ( 45 ).
(a) Ifz= 0anda=
√
x^2 +y^2 Lwhat is it and what should it be?
(b) Ifz= 0anda Lwhat is it and what should it be?
(c) Ifz > Landa→ 0 what is this and what should it be? Be careful with your square roots here.
(d) What is the result of (c) forz L?
9.49 Examine the result in Eq. ( 45 ) (a) for smallL, (b) for largeL, (c) forx^2 +y^2 = 0and|z|> L, (d) as in
(c) butzjust a little bit bigger thanL. The first thing you will have to do is to derive the behavior ofsinh−^1
in various domains and maybe to do some power series expansions. In every case seek an explanation of why the
result comes out as it does.