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1. ### Let (a_n) from (n=1 to∞) be a sequence in R ^k with lim a_n = a. Show that {a_n: n≥1} U {a} is closed.?

... = {a_n: n ≥ 1} U {a}. Suppose x ∈ R ^k \ X. Then x ≠ a and x ≠ a_n for...gt; 2d - d = d > 0, y ≠ a. Therefore y ∈ R ^k \ X. This shows that the open...

2 Answers · Science & Mathematics · 28/11/2013

2. ### Let T consist of ∅ (empty set), ℜ (real numbers) and all intervals (-∞, p) for p ∈ ℜ (real numbers).?

We need to check that: (1) ∅, ℜ are open; (2) T is closed under... open. Otherwise, U(B_i) = ℜ is open. [[you should check these last two claims...

1 Answers · Science & Mathematics · 06/02/2013

3. ### How do I factor r ^5 + 1?

...it has no positive Real roots. When you replace " r " with "- r ", you get, f(- r ) = - r ^5 + 1 and this has one change of...

3 Answers · Science & Mathematics · 20/02/2014

4. ### Sketch the image in the xy-pale of the region R in the first quardent (calculus III, please help?

∫ ∫ r xy^3 dA r : y=x, y=3x, xy=1, xy=4 r is the region enclosed by the lines and the hyperbolas...

1 Answers · Science & Mathematics · 29/07/2010

5. ### Differential Equation word problem - R -C circuit?

Hi impressed voltage = 0 ... Cq + R dq/dt = e(t) q(0) = 0.15 e(t) = 0 Then Cq + R dq...

1 Answers · Science & Mathematics · 23/09/2010

6. ### How is dS/dt related to dr/dt if neither r nor h is a constant?

S= pi* r * ( r ^2+h^2)^(1/2) a) If neither h nor r is a constant, then both dr...and dh/dt will determine how fast the surface area changes. dS/dt = pi* r [ (1/2)( r ^2+h^2)^-1/2 * (2r* dr/dt + 2h*dh/dt) ]+ pi*( r ^2+ h^2)^(1/2)* dr/dt...

1 Answers · Science & Mathematics · 25/03/2013

7. ### Show that R is refexive,antisymmetric and transitive.?

... that the "subset of" in the definition of R includes improper subsets, the reflexiveness of... consider whether (Q,P) can be in R . If so, Qk would have to be a subset of some...

1 Answers · Science & Mathematics · 09/08/2010

8. ### Explain why the numbers of terms in the multinomial expansion of (a1+a2+...+ar)^n is (n+ r -1)C( r -1) ?

...^(n₁) + a₂^(n₂) + ......+ a_ r ^(n_ r ) where n₁ + n₂ + ....+ n_ r = n.....(1...the context of using the formula "n CHOOSE r ". There is no contradiction here, since we...

2 Answers · Science & Mathematics · 17/01/2015

9. ### Permutations, given n find r ?

nPr = n! / (n - r )! 3Pr = 3! / (3 - r )! 3! / (3 - r )! = 3! 3! = 3! * (3 - r )! 1 = (3 - r )! n! = 1 when n = 1 or when n = 0. For the sake of ease, let's just say 3 - r = 1 3 - r = 1 3 - 1 = r 2 = r Pretty much do the same thing for the next...

1 Answers · Science & Mathematics · 31/05/2015

10. ### how to solve 3/4 ( r - 1) = 6 ?

3/4( r -1) = 6 Multiply both sides by 4, to get rid of the fraction (4)3/4( r - 1) = (4)6 3( r - 1) = 24 Use the distributive property to get rid of the ...

3 Answers · Science & Mathematics · 23/02/2010