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--- math104-s21:s:lylekahney [2021/05/11 04:33]
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+++ math104-s21:s:lylekahney [2026/02/21 14:41] (current)
@@ Line 1: / Line 1: @@
-{{ :math104:s:math_104_review_notes_1_2.pdf |}}
+{{ math104-s21:s:math_104_review_notes_1_2.pdf |}}
-{{ :math104:s:math_104_review_notes_2_2.pdf |}}
+{{ math104-s21:s:math_104_review_notes_2_2.pdf |}}
 **__Questions:__** (In reverse order)
-)What is the function d∝?
+)What is the function dα?
 )Why are you allowed to change the variable of integration?
-)Is ∝ a function?
+)Is α a function?
 )Is there a way to show integration is the reverse of differentiation?
@@ Line 15: / Line 15: @@
 )What is a weight function?
-)What's the difference between L(P, f) and L(P, f, ∝)?
+)What's the difference between L(P, f) and L(P, f, α)?
 )If f is bounded, is f always integrable?
@@ Line 27: / Line 27: @@
 )What does def 24 tell us?
-{{:math104:s:screen_shot_2021-05-10_at_8.16.11_pm.png?600|}}
+{{math104-s21:s:screen_shot_2021-05-10_at_8.16.11_pm.png?600|}}
 )What do thm's 5.9 and 5.10 tell us?
-{{:math104:s:screen_shot_2021-05-10_at_8.21.12_pm.png?600|}}
+{{math104-s21:s:screen_shot_2021-05-10_at_8.21.12_pm.png?600|}}
 )When is pointwise continuity useful?
@@ Line 57: / Line 57: @@
 )How do you prove a set is compact?
-)Can.a set be closed and bounded but not compact?
+)Can a set be closed and bounded but not compact?
-)
+)Why is S open in S?
-)
+)Does a distance function apply to functions?
-)
+, 29, 30)
-)
+{{math104-s21:s:screen_shot_2021-05-10_at_9.35.43_pm.png?600|}}
-)
+)If you want to prove the limit of a sequence can you use sequential limits?
-)
+)Can you have a subsequence with one term?
-)
+)Can you have a subsequence with infinite terms?
-)
+)Is a constant function increasing or decreasing?
-)
+)Does a function need to be oscillating to be Cauchy?
-)
+)If lim t<sub>n</sub>=s and s<sub>n</sub>=s does t<sub>n</sub>=s<sub>n</sub>?
-)
+)Is {r ∈ Q : r ≤ a} a set of r's or a's?
-)
+)What's the difference between R ∪ {-∞, ∞} and just R?
-)
+)What properties of R hold for {-∞, ∞}
-)
+)Why is [a, ∞) closed?
-)
+)Are -∞ and ∞ bounds for infinite sets?
-)
+)Does the completeness axiom hold for complex numbers?
-)
+)Can sup and inf be elements of S?
-)
+)Do sup and inf work in any plane?
-)
+)How do we know there aren't any gaps in R?
-)
+)Does the triangle inequality hold for higher dimensions of R?
-)
+)How does a number r satisfy the Rational Zero Theorem?
-)
+, 49)
-)
+{{math104-s21:s:screen_shot_2021-05-10_at_9.49.08_pm.png?600|}}
-)
+)Why don't we use a base 7 number system?
-)
-**__Answers:__**

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