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Complex Proof

  1. Dec 20, 2006 #1
    If f(x)>0 for all xElement-ofsymbol [a,b], then
    b
    Integral sign f>0
    a

    a) Give an example where f(x)>0 for all xElement-ofsymbol [a,b], and f(x)>0 for some xElement-ofsymbol [a,b], and

    b
    Integral sign f=0
    a

    b) Suppose that f(x)>0 for all xElement-of symbol[a,b] and f is continous on at x0 in [a,b] and f(x0)>0. Prove that

    b
    Integral sign f>0
    a
     
    Last edited: Dec 20, 2006
  2. jcsd
  3. Dec 20, 2006 #2

    quasar987

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    "elements of" is written in words as "in" (ex: for all x in A,...)

    As worded, these questions are both equivalent to

    "Show that if f f(x)>0 for all xElement-ofsymbol [a,b], then
    [tex]\int_a^bfdx>0[/tex]"

    But this is precisely the statement of the result you cited in the begining, so the questions are not challenging at all and contain unnecessary words.
     
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