Question

need improper integrals (converging/diverging) help...

Answer 1

need help with whats going on from after the 2nd equals sign in (ii).... the ln(ln(2)) - ... part. Any help will be appreciated.

Answer 2

im not sure how they are presenting that thing

Answer 3

essentially, you take the limit of the integration as "t" approaches the offensive part

Answer 4

for example:

\[\int_{0}^{1}\frac{1}{x}dx=\lim_{t\to\ 0}\int_{t}^{1}\frac{1}{x}dx\]

Answer 5

if the limit exists, it converges; if not, then it diverges

Answer 6

but why does ln(ln 2) - ln(ln a) -->1 as a --> 1+

Answer 7

i mean ...ln(ln(a)) --> inf ...

Answer 8

what is \[\log0\]?

Answer 9

for the sake of clarity

as a goes to 1; ln a goes to 0 since ln(1) = 0

ln(0) approaches - inf

-(-inf) = inf

Answer 10

ooooooooooooh....i drew a picture of the ln graph and i get it. sorry....was being stupid.

Answer 11

Thanks for the responses :)

Answer 12

;) pictures do help alot when you can draw them