anonymous
  • anonymous
Prove the theorem that if limx→d h(x) = P and limx→d k(x) = Q and h(x) ≥ k(x) for all x in an open interval containing d, then P ≥ Q by using the formal definition of the limit, showing all work.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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apoorvk
  • apoorvk
|dw:1332434727006:dw| in the interval (m,n) since h(x) is greater than k(x) everywhere, for any value of x, therefore for any limit of x=d it sis valid too, since d is a member of the interval (m,n), and limts of d lie in the interval too. use proper statements to get a "hence, proved" at the end
TuringTest
  • TuringTest
I think they wanted delta-espsilon stuff though... which means I'm out!
across
  • across
Whoops, sorry about that. Well, let's see...

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across
  • across
... are you still there?
across
  • across
Perhaps you know that\[f(x)\geq0\text{ in a neighborhood of }d\text{ and }\lim_{x\to d}f(x)=L\implies L\geq0.\]To solve your problem, you can use that with \(f(x)=h(x)-k(x)\) and \(L=P-Q\). All that you are left to do is prove the above by contradiction.

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