math104-s21:s:dingchengyang
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math104-s21:s:dingchengyang [2021/05/09 22:29] 73.132.71.37 |
math104-s21:s:dingchengyang [2026/02/21 14:41] (current) |
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| 13: Let f : [a, b] → R be a Riemann integrable function. Let g : [a, b] → R be a | 13: Let f : [a, b] → R be a Riemann integrable function. Let g : [a, b] → R be a | ||
| function such that {x ∈ [a, b]; f(x) = g(x)} is finite. Show that g(x) is Riemann integrable and the integral of f(x) on [a,b] is equal to that of g(x). Does the conclusion still hold when {x ∈ [a, b]; f(x) = g(x)} is countable? | function such that {x ∈ [a, b]; f(x) = g(x)} is finite. Show that g(x) is Riemann integrable and the integral of f(x) on [a,b] is equal to that of g(x). Does the conclusion still hold when {x ∈ [a, b]; f(x) = g(x)} is countable? | ||
| - | 14: When do we have equality in the inequality |integral f| <= integral |f| ?\\ | + | 14: When do we have equality in the inequality |integral f| < = integral |f| ?\\ |
| 15: What are ways of proving connectedness? | 15: What are ways of proving connectedness? | ||
| 16: What is the epsilon room proof?\\ | 16: What is the epsilon room proof?\\ | ||
math104-s21/s/dingchengyang.1620599393.txt.gz · Last modified: 2026/02/21 14:44 (external edit)
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