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--- math104-s21:s:lylekahney [2021/05/11 03:09]
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-{{ :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 dα?
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+)Why are you allowed to change the variable of integration?
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+)Is α a function?
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+)Is there a way to show integration is the reverse of differentiation?
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+)What is a weight function?
-)
+)What's the difference between L(P, f) and L(P, f, α)?
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+)If f is bounded, is f always integrable?
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+)If f has infinitely many discontinuities on an infinite interval is it not integrable?
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+)Is Taylor's theorem an estimate of higher derivatives?
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+)Does Taylor's theorem only tell you higher derivatives at a single point or an interval?
-)
+)What does def 24 tell us?
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+{{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?
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+{{math104-s21:s:screen_shot_2021-05-10_at_8.21.12_pm.png?600|}}
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+)When is pointwise continuity useful?
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+)What are running bumps?
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+)How can a set be both open and closed?
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+)What is the minimum number of elements needed in an interval?
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+)How is lim x→as different from lim x→a
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+)Can you take the limit of a distance function?
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+)Does p have to be an element of E? as its a limit point
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+)If f(I) is continuous and not strictly increasing, is the inverse of f still continuous?
-)
+)What is a partial sum?
-)
+)For the comparison test to the series have to be similar?
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+)If lim a<sub>n</sub>=a does the infinite series a<sub>n</sub> converge?
+)How do you prove a set is compact?
-**__Answers:__**
+)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?

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