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#1 Exercises » Integration of inverse functions » 2012-03-06 15:06:46
- Kryptonis
- Replies: 1
Could use a hint on how to begin this problem:
∫cos^-1 (x) dx
#2 Re: Exercises » Integration with Inverse Trig function » 2012-03-06 14:46:24
Thanx a bunch, was totally going in the wrong direction on this
#3 Exercises » Integration with Inverse Trig function » 2012-03-04 20:49:50
- Kryptonis
- Replies: 10
I'm having a bit of a time with this. I have tried integration by parts and just can't seem to get it right....
∫(3-3x)/(sqrt(64-9x^2)) dx
#4 Help Me ! » Length of a curve » 2011-03-11 22:06:12
- Kryptonis
- Replies: 2
x = t / (3+t) y = ln(3 + t) 0 ≤ t ≤ 4
Here's the problem, my real question lies in the answer...
-sqrt(u^2 + 9)/(u) + ln(u + sqrt(u^2 + 9)) with the lower @ 3 and the upper @ 7
where u = t + 3 and du = dt
When I integrate, I'm at a loss as to how i should be coming up with -sqrt(u^2 + 9)/(u) + ln(u + sqrt(u^2 + 9)).
As I keep coming up with -sqrt(u^2 + 9)/(u) + ln(sqrt(u^2 + 9).
#5 Re: Help Me ! » set help » 2011-03-10 16:05:12
Ty, got this one shortly after i posted. Thanx for the help though. Much appreciated!
#6 Re: Help Me ! » functions » 2011-03-10 16:02:58
ty sir, much appreciated!
#7 Re: Help Me ! » set help » 2011-03-04 02:13:14
Figured it out...
A − B ⊆ C ≡ (A ∩ ¬B) ⊆ C Def of Diff
≡ {x | (x ∈ A ∧ x ¬∈ B) → x ∈ C} Def of Diff, Def of subset
≡ {x | (x ¬∈ A ∨ x ∈ B) ∨ x ∈ C} Log Equiv, De Morg
≡ {x | (x ∈ A → x ∈ B) ∪ x ∈ C} Log Equiv, Def of Union
≡ A ⊆ B ∪C Set Builder Notation
#8 Help Me ! » set help » 2011-03-04 01:25:35
- Kryptonis
- Replies: 1
Let A, B and C be arbitrary sets taken from the positive integers.
Prove the following statement: If A − B ⊆ C , then A ⊆ B ∪C
#9 Help Me ! » functions » 2011-03-04 01:24:29
- Kryptonis
- Replies: 3
a) Determine which of the followings are functions with domain X.
i) (3 pts) X = {1, 3, 5, 7, 8} and R ={(1,7), (3,5), (5,3), (7, 7), (8,5)}
ii) (3 pts) X = {-2, -1, 0, 1} and R = {(-2, 6), (0, 3), (1, -1)}
iii) (3 pts) X is the set of real numbers and, for x ∈ X,
g(x) = x^2 − 3x + 2, assume that the codomain is also X
iv) (3 pts) X is the set of real numbers and, for x ∈ X,
g(x) = sqrt(x^2 − 3x + 2) , assume that the codomain is also X
v) (3 pts) X is the set of real numbers and, for x ∈ X, g(x) = log2 x , , assume that the codomain is also X
b) Let Z = {...−2, −1, 0, 1, 2, ...} denote the set of integers. Suppose f : Z→Z is a function, defined by:
f (n) = {2 if is odd
n/ 2 if is even
i) (5pts) Prove or disprove that f is one-to-one (injective)
ii) (5pts) Prove or disprove that f is onto (surjective).
#10 Help Me ! » set help » 2011-03-04 01:22:41
- Kryptonis
- Replies: 2
Prove the following assertions for sets A and B from an universe U without using Venn Diagrams or membership tables:
a) (10 pts) A ⊆ B if and only if A ∩ ¬B = ∅.
b) (10 pts) A ⊆ B if and only if ¬A ∪ B = U.
#11 Help Me ! » Set operations, proof » 2011-03-03 16:27:07
- Kryptonis
- Replies: 1
Let A, B, and C be sets such that C ⊂ B (i.e., C is a proper subset of B, or possibly C = B). Use appropriate set theoretic laws and theorems to prove that (A B) ∪ (B C) = ¬C ∩ (A ∪ B). Be sure to explain each step of your proof.
This is what i have, and i have tried several ways just can't quite seem to get it right... 
Any help would be great, ty in advance!
(A B) ∪ (B C)
≡{x | x ∈ A ∧ x B}∪{x | x ∈ B ∧ x C} Def of diff
≡{x | (x ∈ A ∧ x B) ∨ ( x ∈ B ∧ x C)} Def of union
≡{x | (x ∈ A ∧ x B) ∨ ( x B ∨ x ∈ C)} De Morgan
≡{x | x ∈ A ∧ (x B ∨ x ∈ C)} Idem & Assoc
≡{x | x ∈ A ∧ (x ∈ B ∧ x C)} De Morgan
≡{x | x C x ∧ (∈ A ∧ x ∈ B)} Assoc
≡{x | x C x ∩ (∈ A ∩ x ∈ B)} Def of Inter
≡ ¬C ∩ (A ∩ B) Def of Set Build Notation
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