#1 is a theorem. You should see if you could prove it. It is actually very important.
#2: On [0,1] consider
Hello, Gracy!
State true and false.
(1) If and are continuous and for ,
then: .
I would say True . . .Code:| * | :* : | : * : | : * : | : * f(x) | : : | : o g(x) | : o : | : o : | o : --+---+---------+-- | a b
If is always "above" on
. . then the area under will be the area under
(2) If and are continuous and for ,
then: . for
This is False . . .Code:| * | :* : | : * : | : * : | : * f(x) | : : | : o g(x) | : o : | : o : | o : --+---+---------+-- | a b
While is above , we see that
. . is negative while is positive.