1. ## convergent/divergent integrals

Suppose f and g are continous functions with f(x)  g(x)  0 for x  a then
(A) If integral a to infinity f(x) dx is convergent, then integral a to infinity g(x) dx is convergent
(B) If integral a to infinity f(x) dx is divergent, then integral a to infinity g(x) dx is divergent
(C) If integral a to infinity f(x) dx is convergent, then integral a to infinity g(x) dx is divergent
(D) If integral a to infinity f(x) dx is divergent, then integral a to infinity g(x) dx is convergent

i have no idea on this one..

2. Originally Posted by buttonbear
Suppose f and g are continous functions with f(x)  g(x)  0 for x  a then
(A) If integral a to infinity f(x) dx is convergent, then integral a to infinity g(x) dx is convergent
(B) If integral a to infinity f(x) dx is divergent, then integral a to infinity g(x) dx is divergent
(C) If integral a to infinity f(x) dx is convergent, then integral a to infinity g(x) dx is divergent
(D) If integral a to infinity f(x) dx is divergent, then integral a to infinity g(x) dx is convergent

i have no idea on this one..
Can't read your inequalities in the first part. CAn you tell me what those are?

3. I think is $f(x)\ge g(x)\ge0$ which can be rewritten backwards as $0\le g(x)\le f(x).$

Following up on this, only these statements hold:

1) If $f(x)$ converges, then so does $g(x).$

2) If $g(x)$ diverges, then so does $f(x).$

4. thank you so much

i actually just learned this today, and it's on my midterm tomorrow