- #1

Dell

- 590

- 0

[tex]\int[/tex]dx/[tex]\sqrt[3]{x}[/tex](e

^{e}-e

^{-x})

i am asked if it comverges or diverges,

what i have learned is that if i can find :

-a similar function that is bigger than my function and that i know converges, then my function also converges

-a similar function that is smaller than my function and that i know dicerges, then my function also diverges

-a function g(x) such that

lim f(x)/g(x)=K, (K not 0, not infinity) then f(x) acts like g(x)

x->inf

my similar function g(x) is 1/3[tex]\sqrt[3]{x}[/tex] which is smaller than f(x), BUT my g(x) converges, so that doesn't prove anything according to the 1st 2 conditions,

generally can i use the 3rd condition even though my integral is from 0 to 1 and not to infinity??

in this case that too doesn't work. what can i do from here??

if not how would you solve this?