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3. Best strategies to get motivated?

I don't think that motivation will make you work around the clock, work ethic will. I once heard someone along the lines: Motivation gets the ball rolling, work ethic/discipline keeps the ball rolling. That being said i think best way to develop work ethic is to develop work habits. Since you...
4. Check my solution for discontinuous function

Homework Statement Let f: R -> R and defined with f(x)={ x, if x \in Q or x^2 if \in R\Q} a) Prove that function is discontinuous at x=2; b) Find all points for R in which function is continuous; The Attempt at a Solution As far as i know there are infinitely many irrationals but more...
5. Baby Rudin Theorem 1.11

Since you gave counter example you assumed that S is an order set with least-upper-bound property. (Right?) If so then this means that if E is subest of S, and E is non empty and E is bounded above , then sup E exists in S. So let S = (0,1) ##\cup## (2,3) and Let E= (2,3). E is subset of S...
6. Baby Rudin Theorem 1.11

If i may usk where does least-upper-bound property come into play in your counter example?
7. Baby Rudin Theorem 1.11

Theorem: Suppose S is an ordered set with the least-upper-bound property, B⊂S, B is not empty, and B is bounded below. Let L be the set of all lower bounds of B. Then α=supL exists in S, and α=infB. Rudin proves that α=supL, α is an element of L and that α=infB. For α to be sup i.e. lub it...
8. Can this be considered a proof

Good points, there goes my proof in the water.:cry:
9. Can this be considered a proof

Homework Statement If p is a prime and k is an integer for which 0<k<p, then p divides \displaystyle \ \binom{p}{k}. Whne p divides \displaystyle \ \binom{p}{k} it means that \displaystyle \ \binom{p}{k}=p*b. wheren b is some number. The Attempt at a Solution So p is equal to some number k...
10. Post Your Summer/Fall 2013 Class Schedules

Fall Semester: 1. Analysis 1A 2. Linear Algebra A 3. Programming 1 4. Introduction to Mathematical Logic 5. English 1

12. How do you solve eq. that have both exponents and polynomials

The question was: How many real number solutions are there for 2^x=-x^2-2x. I tired for an hour to isolate x but i couldn't do it. Then i used wolfram alpha and it gave me two solutions and graph. I realized that question was, how many not what are the solutions, and i could do that by graphing...
13. Arithemtic and geometric progession

Homework Statement Numbers a,b,c are consecutive members of increasing arithmetic progression, and numbers a,b,c+1 are consecutive members of geometric progression. If a+b+c=18 then a^2 +b^2 + c^2=? The Attempt at a Solution a + b + c= 18 a + a +d +a + 2d = 18 3a + 3d = 18 3(a+d)= 18...
14. Geometric and arithmetic series

As i have understood it there exist separate arithmetic and separate geometric progression. This is a first time i hear of arithemtico-geometric series.
15. Geometric and arithmetic series

Wel its evident that two solutions are 1 and - 1 but what kind of geometric progression is with r=1 or r=-1?
16. Geometric and arithmetic series

Homework Statement If a,b,c, are at the same time fifth, seventh and thirty seventh member of arithmetic and geometric progression then a^{b-c}b^{c-a}c^{a-b} is: The Attempt at a Solution I tried solving system of equations but i have four unknown. I was able to reduce it to on unknown...
17. Combinatorics problem

Homework Statement Let X be a set containing all four digit numbers made up of {1,2,3}, where every number contains every digit at lease once. Number of all subsets is: The Attempt at a Solution So firs i have to find number of elements in the set: 3!*3 + 3*12 = 54 Now what they...
18. Best way self study real analysis?

So you mean to use Spivak's textbooks instead of Abbott or to just add Spivak to the mix? I know that Rudin doesn't have great rep for user friendliness. I thought using Abbott first as an intro and then to study Rudin.
19. Best way self study real analysis?

In October of this year i will start with math major and i decided to prepare myself in spear time. In my faculty there is no such thing as Calculus but rather you go strait to the analysis and you pick up calculus along. (There is singe variable calculus in high school). In first two years...
20. Creating new organs for transplantation?

Is there planned research that tries to create new organ for transplantation? So when someone needs a new organ e.g. kidney, instead of finding a donor, scientists could create an organ form stem cells perhaps. Is this even psychically possible? Reason i ask this question is that i watched...
21. Find equation of a cricle

Thank you everyone i solved the problem.
22. Find equation of a cricle

Well i know that center is at x=3. I know that the slope between A and B is -√3 (3-3-√3)/(1) If i want to find a line that goes throug the points it should be like this: For A: y-0=-√3(x-3) y=-√3x + 3√3 but for B i get different line y+1=-√3(x-3 -√3) y=-√3x + 3√3 +2 Two different lines...
23. Find equation of a cricle

Homework Statement Find the equation of a cricle if it touches x-axis in A(3,0) and it contains B(3 + √3, -1) The Attempt at a Solution Is there a piece of data missing here? Because i can't see how can i find center of circle.
24. Proof of combinations

I managed to prove this without much problem. Probably it is a typo in my textbook.
25. Proof of combinations

Maybe i will try to slove it, This problem should be difficult according to my textbook, here is a pic from my textbook: http://img444.imageshack.us/img444/8316/img00121201304241927.jpg [Broken]
26. Proof of combinations

Yea, i overlooked that. With that in mind. Let n=m=2 \frac{2!}{2!(2-2)!} = \frac{2!}{(2-2)!(2-2 + 2)!} + 2* \frac{(2-1)!}{(2-1)!(2-2)!} + \frac{(2-2)!}{(2-2)!(2-2)!} \frac{1}{1(0)!} = \frac{1}{(0)!1} + 2* \frac{1}{1(0)!} + \frac{(0)!}{(0)!(0)!} 1 = 1 + 2 + 1 1 = 4
27. Proof of combinations

That is exactly what i need to prove, i just didn't know how to write it like that using Latex. Here is full text of problem: Prove that \displaystyle \ \binom{n}{m}=\binom {n} {m-2}+2\binom {n-1} {m-1}+\binom {n-2} {m-2}\ n\geq2, m \geq2 When i plug in n=m=2 i get \frac{0}{0} =...
28. Proof of combinations

After that i get (n-2)!*(n(n-1)(m-1) + 2(n-m+2)(n-m+1)(n-1) + (m-1)(n-m+2)(n-m+1))/(m-1)!(n-m+2)! i tried and i can't find any other common factor in numerator and i have common factors between two products such as (n-1) , (m-1), (n-m+2)(n-m+1). Only other way is to multiply everything and then...
29. Proof of combinations

If i want get whole expression under one fraction i should multply first fraction with (m-1)/(m-1) to get n!(m-1)/(m-1)!(n-m+2)! , second fraction with (n-m+2)(n-m+1)/(n-m+2)(n-m+1) to get (n-1)!(n-m+2)(n-m+1)/(m-1)!(n-m+2)! , and third with (m-1)(n-m+2)(n-m+1)/(m-1)(n-m+2)(n-m+1) to get...
30. Proof of combinations

I don't understad why, since (m-2)! doesn't contain (m-1) nor (n-m)! contains (n-m+2)! or (n-m+1)!
31. Proof of combinations

(m-1)!(n-m+2)!
32. Proof of combinations

I rechecked it two or three time i really don't see how it is wrong.
33. Proof of combinations

I know that, but where to use it?
34. Proof of combinations

Homework Statement Prove the following: \frac{n!}{m!(n-m)!} = \frac{n!}{(m-2)!(n-m + 2)!} + 2* \frac{(n-1)!}{(m-1)!(n-m)!} + \frac{(n-2)!}{(m-2)!(n-m)!} The Attempt at a Solution I tried writing following \frac{n!}{m!(n-m)!} = \frac{n!}{m!(n-m)!}(\frac{m(m-1)}{(n-m + 2)(n-m +...
35. Permutations problem

Homework Statement 1.) 4 of the books have red covers, 3 have green covers, and another 2 have gray covers. In how many ways can the books be arranged on a shelf if books of the same color must be arranged together? The Attempt at a Solution 1) I think that the answer here is 3...
36. Ellipse analyticaly geometry problem

Homework Statement Find parameter a so that line y=ax + 11 touches ellipse 3x^2 + 2y^2 = 11 The Attempt at a Solution| I can rewrite ellipse equation like \frac{x^2}{\frac{11}{3}} + \frac{y^2}{\frac{11}{2}} = 1 And i know that line y=kx + n touches ellipse when a^2k^2 + b^2 = n^2...
37. Proving \frac{a+b}{2}\geq\sqrt{ab} for 0 < a \leq b

Well i thought that since b≥ (a+b)/2 and (a+b)/2 * b = ((a+b)/2)^2 (because it can be b = (a+b)/2)
38. Proving \frac{a+b}{2}\geq\sqrt{ab} for 0 < a \leq b

Homework Statement Show that \frac{a+b}{2}\geq\sqrt{ab} for 0 < a \leq b The Attempt at a Solution Since b \geq a then b + a \geq 2a and 2b\geq a + b That is \frac{a+b}{2}\geq a and \frac{a+b}{2}\leq b. Since \frac{a+b}{2}\leq b can i multiply \frac{a+b}{2}\geq a with b? If...
39. Integration problem

Homework Statement Integrate \int3^x\cos x\,dx The Attempt at a Solution It has to be done using partial integration. I don't know what should be u?
40. Did anyone else had self doubt?

Hello friends. It seems to me that i have reach a wall with my math education. In 3.5 months i will be doing tests for mathematics faculty(college), something like SAT but a bit more difficult i think. Anyway i have been doing more difficult problems from problem set and i simply can't figure...
41. Graphing a function

I figured it out by myself when i sketched graph. My professor didn't mention local max and min, he only talked about absolute. Thank you anyway.
42. Graphing a function

Homework Statement I should sketch function (x^2 + x -12)/(x-4). The Attempt at a Solution I have problem with first derivative i find it to be (x^2 - 8x +8)/(x-4)^2 with roots at 4 - 2√2, 4 + 2√2, and 4(we lose four because f is not defined at 4). Where at 4 - 2√2 f is at max and...
43. Suggestion Alternative ways to subscribe

I have been using physics forum for good year and a half now for homework problems and for asking for advice, so i wanted to subscribe but it is only possible to do it over paypal, but in Serbia where i live we don't have paypal so i can't do it. Is there any other way to subscribe and if not it...
44. Is QM truly random and many world theory

Exactly that kind of the system is not random, for me truly random system is system that you can't possibly predict, even if you have all the possible data and know all the laws of physics.
45. Is QM truly random and many world theory

Hi everybody, i didn't wanted to create two separate threads so merged them into one. i got confused watching Brian Green explaining QM on one of his shows. He compared distribution in double slit experiments with throwing a ball on a roulette. He said that casino doesn't have to know...
46. Baby Rudin problem

Homework Statement Let f be defined for all real x and suppose that, \left|f(x) - f(y)\right|\leq(x-y)^2 for all real x and y. Prove that f is constant. The Attempt at a Solution First of all, is following allowed. Since f is constant then \left|f(x) - f(y)\right|=0, and form here to build...
47. Application of derivatives to geometry

:cry::cry: I can't believe it. I spent almost 2 hours on this silly problem because of silly mistakes. Thank you.:smile:
48. Application of derivatives to geometry

So M^{'}=Pi*(\sqrt{(2R)^2 - H^2}) + \frac{Pi*H}{2*\sqrt{(2R)^2 - H^2}}*(8R -2H) M^{'}=Pi*(\sqrt{(2R)^2 - H^2}) + \frac{Pi*H*(4R - H)}{\sqrt{(2R)^2 - H^2}} M^{'}=Pi*((\sqrt{(2R)^2 - H^2}) + \frac{H*(4R - H)}{\sqrt{(2R)^2 - H^2}}) M^{'}=Pi*((\sqrt{(2R)^2 - H^2}) + \frac{H*(4R -...
49. Application of derivatives to geometry

Homework Statement Of all cylinders inscribed in sphere of radius R largest area of side(M) has cylinder which hight is R\sqrt{2}. Prove. The Attempt at a Solution I understand how to prove this i only have problem with derivative: M=2*r*Pi*H and r=\frac{\sqrt{(2R)^2 - H^2}}{2}...
50. Another arithmetic progression problem

I don't understand, how come a1 + a2 + a3= a1 + a1 +d + a1 + 2d = 3a1 + 2d and not 3a1 + 3d. What happened to that one d