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math104-s21:s:antonthan [2021/05/07 17:12]
45.48.153.5 [Problem 18]
math104-s21:s:antonthan [2022/01/11 18:30] (current)
24.253.46.239 ↷ Links adapted because of a move operation
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 U(f)supn(U(f,Pn))=limRn=infn(L(f,Pn))L(f)U(f) \leq \sup_n(U(f, P_n)) = lim R_n = \inf_n(L(f, P_n)) \leq L(f) U(f)supn(U(f,Pn))=limRn=infn(L(f,Pn))L(f)U(f) \leq \sup_n(U(f, P_n)) = lim R_n = \inf_n(L(f, P_n)) \leq L(f)
  
-Since we also have L(f)=U(f)L(f) = U(f) by integrability, $lim R_n = \int_a^f(x)dx$, as desired.+Since we also have L(f)=U(f)L(f) = U(f) by integrability, $lim R_n = \int_0^f(x)dx$, as desired.
  
 === (b) === === (b) ===
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 ===== ඞ ඞ ඞ ඞ ඞ ===== ===== ඞ ඞ ඞ ඞ ඞ =====
-{{ :math104:s:amongus.mp4 |}}+{{ math104-s21:s:amongus.mp4 |}}
math104-s21/s/antonthan.1620432766.txt.gz · Last modified: 2021/05/07 17:12 by 45.48.153.5