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

Question

anonymous · Answer

attachment

anonymous · Answer

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

amistre64 · Answer

im not sure how they are presenting that thing

amistre64 · Answer

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

amistre64 · Answer

for example:

$$\int_{0}^{1}\frac{1}{x}dx=\lim_{t\to\ 0}\int_{t}^{1}\frac{1}{x}dx$$

amistre64 · Answer

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

anonymous · Answer

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

anonymous · Answer

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

turingtest · Answer

what is $$\log0$$?

amistre64 · Answer

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

anonymous · Answer

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

anonymous · Answer

Thanks for the responses :)

amistre64 · Answer

;)  pictures do help alot when you can draw them