Analysis 2 HELP!

  • Thread starter Misswfish
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Suppose f is continuous function on [a,b] such that for each continuous function g, [tex]\int[/tex](fg)dj = 0 (Note: integral is from a to b) , then f(x) = 0 for each x in [a,b].

I know that I should use the theorem If is continuous on [a,b], f(x)[tex]\geq[/tex]0 for each x in [a,b] and theree is a number p i n [a,b] such that f(p) > 0, THen [tex]\int[/tex]f dj > 0.

I just dont understand how they tie together.
 

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  • #2
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I know that I should use the theorem If is continuous on [a,b], f(x)[tex]\geq[/tex]0 for each x in [a,b] and theree is a number p i n [a,b] such that f(p) > 0, THen [tex]\int[/tex]f dj > 0.
What is the contrapositive of this statement? It pretty much falls out of it.
 
  • #3
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Ahhh my teacher told me to pick a "clever" g(x) so that we can use this theorem and therefore f(x) = 0. I was thinking contradiction but my teacher shot that down
 

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