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Most popular questions and responses by mathstudent
1. math

Find the least squares approximation of x over the interval [0,1] by a polynomial of the form a + b*e^x --------------------------------------------------------- The polynomial produces an output space with two linearly independent basis vectors: u1 = 1,

2. math

How do I derive the secant reduction rule? Integral (sec x)^n dx = Integral (sec x)^(n-2) * (sec x)^2 dx = Integral ((tan x)^2 + 1)^(n/2-1) * (sec x)^2 dx Doing a substitution with: u = tax x du = (sec x)^2 dx = Integral (u^2 + 1)^(n/2-1) * du At this

3. calculus

Assuming that: Definite Integral of e^(-x^2) dx over [0,infinity] = sqrt(pi)/2 Solve for Definite Integral of e^(-ax^2) dx over [-infinity,infinity] I don't know how to approach the new "a" term. I can't use u-substitution, integration by parts, partial

4. math

How do I derive the secant reduction formula? Am I asking this question wrong? Integrate: (sec x)^n dx

5. math

Prove that if A is a symmetric n x n matrix, then A has a set of n orthonormal eigenvectors. http://ltcconline.net/greenl/courses/203/MatrixOnVectors/symmetricMatrices.htm I've read the entire page and while it's on the correct topic, it doesn't prove what

6. Trigonometry

There is an arbitrary triangle with angles A, B, and C and sides of lengths a, b, and c. Angle A is opposite side a. How do I get the formulas: b * cos C + c * cos B = a c * cos A + a * cos C = b a * cos B + b * cos A = c Are these standard trig formulas?

7. statistics

sigma is the standard deviation of a population of size N S is the standard deviation of a sample of size n from within the population. What is the estimated value of S^2? If the population was infinitely large (size N = infinity), what would the estimated

8. calculus

Integrate: dx/(2x^2 + 4x + 7)

9. math

If A^TA is an invertible matrix, prove that the column vectors of A are linearly independent. You know that if statement X implies statement Y then that is equivalent to Not(Y) implies Not(X). You can start by taking the column vectors of to be linearly

10. math

A trigonmetric polynomial of order n is t(x) = c0 + c1 * cos x + c2 * cos 2x + ... + cn * cos nx + d1 * sin x + d2 * sin 2x + ... + dn * sin nx The output vector space of such a function has the vector basis: { 1, cos x, cos 2x, ..., cos nx, sin x, sin 2x,

11. Question

Dear experts, What is your motivation to provide all this help? I'm extremely grateful for this service, but why do you help so much? Are you paid to do this? Are you teachers who like to assist in spare time? Trying to brush up on your own skills? Thanks!

12. calculus

Integrate x/(x^2 + 4) dx via trig substitution and by u=x^2+4 substitution. Show that results are equal. Via trig substitution of x=2 *tan t, I get: 1/2 * tan^-1 (x/2) + c Via u = (x^2 + 4) substitution, I get: 1/2 * ln |x^2 + 4| + c How are these equal?

13. linear algebra

Prove that the trace is a similarity invariant. In other words, if two matrices are similar, then they must have the same trace. Got the answer from Wikipedia: tr(AB) = tr(BA) tr(ABC) = tr(CAB) tr(P^-1 * A * P) = tr(P^-1 * P * A) = tr(A)

14. math

Prove that if A is a diagonalizable matrix, then the rank of A is the number of nonzero eigenvalues of A. http://ltcconline.net/greenl/courses/203/MatrixOnVectors/symmetricMatrices.htm I've read the entire page and while it's on the correct topic, it

15. math

Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2

16. math

I've finished studying a full textbook on linear algebra and another on statistics. I've done most of the practice problems and I understand everything covered in these books very well. But I need to know more. Specifically, I'd like to understand more

17. math

Integrate: y/sqrt(2y+1) dx

18. linear algebra

if: A and B are matrices and A^2 is similar to B^2 Is A guaranteed to be similar to B? ------- Matrix similarity means that the matrices are identical if one of the matrices is converted to another basis. If matrices C and D are similar: C = P^-1 * D * P

19. Math: Linear Algebra

Let T1: P1 -> P2 be the linear transformation defined by: T1(c0 + c1*x) = 2c0 - 3c1*x Using the standard bases, B = {1, x} and B' = {1, x, x^2}, what is the transformation matrix [T1]B',B T(c0 + c1*x) = 2c0 - 3c1*x ---> T(1) = 2 T(x) = -3x So, the matrix

20. Calculus

Suppose that the region between the x-axis and the curve y=e^-x for x>=0 has been revolved around the x-axis. Find the surface area of the solid. I got 3*pi The book shows an answer of pi * [sqrt(2) + ln(1 + sqrt(2))] Where do I go wrong? For the sides of

21. Calculus

My book says to do the following problem via computer and via hand: Calculate the definite Integral of e^-x * cos x dx over (0, +infinity) My TI-89 calculator gets 1 (it gets the same thing when I replace infinity with 999). when I do this by hand, I get:

22. Calculus

Calc length of arc of y=ln(x) from x=1 to x=2 ---- So far: Definite Integral over x=(1,2) of sqrt(1 + 1/x) dx 1/x = tan^2 t x = 1/tan^2 t sqrt(1+1/x) = sqrt(1+tan^2 t) = sec t dx = -2 * tan^-3 t * sec^2 t dt Integrate over x=(1,2): sec^3 t / tan^3 t dt

23. calculus

Integrate: dx/sqrt(x^2-9) Answer: ln(x + sqrt(x^2 - 9)) + C I'm getting the wrong answer. Where am I going wrong: Substitute: x = 3 * sec t sqrt(x^2 - 9) = sqrt(3) * tan t dx = sqrt(3) * sec t * tan t Integral simplifies to: sec t dt Integrates to: ln|sec

24. calculus

Calculate definite integral of dx/(x^4 * sqrt(x^2 + 3)) Over (1,3) I start with the substitution x = sqrt(3)*tan t so: sqrt(x^2 + 3) = sqrt(3) * sec t dx = sqrt(3) * sec^2 t dt x^4 = 9 * tan^4 t The integral simplifies to: = dt/(tan^3 t * sin t) How do I

25. math

Show that if x is a nonzero column vector in R^n, then the nxn matrix: A = I - 2/||x||^2 * xx^T is orthogonal. Notation key: ||x|| = norm of x x^T = transpose of x I = identity matrix. Let me try to convince a math student to use "physics" notations that

26. math

I read from my textbook: If S is the infinite series 1 + x + x^2 + x^3 + ... Then Sx = x + x^2 + x^3 + x^4 + ... = S - 1 So, S = 1/(1-x) I follow what that logic, but it still doesn't make sense. The way I see it, if you plug any real number > 1 into x, S

27. Calculus

Suppose that ax^2 + bx + c is a quadratic polynomial and that the integration: Int 1/(ax^2 + bx + c) dx produces a function with neither a logarithmic or inverse tangent term. What does this tell you about the roots of the polynomial?

28. math

Integrate: csc x dx

29. calculus

How do I derive the integration reduction formula for tangent? Integral of (tan x)^n dx = ... I can do the derivations for sin/cosine, but I'm getting stuck on tan. Thanks!

30. math

I'm reading a formula (lots of greek letters) and I see a symbol that looks like a backward six. That doesn't seem to be any greek letter... What is it?

31. Calculus

Integrate e^(-x^2/2) dx What branch of calculus is this? Is this differential equations?

32. math

Find the arc length of y = ln(cos x) over x = [0, pi/4]

33. Calculus

integrate: (x^2 + 1)^k dx

34. math

Integrate: (sin 2x)^3 dx I can see the answer, but how do I do this?

35. math

Prove limit as x approaches +infinity of (1 + 1/x)^x = e

36. math

I'm having a little trouble understanding the difference between the codomain and the range of a function. I'm reading the Wikipedia article on Codomain (I can't post the URL), but it doesn't make sense. I understand what they are saying and it still

37. math

Factor: x^3 - 3/4x - 1/4 The answer is: (x - 1)(x + 1/2)^2 How do I learn to do that? I'd like to reread an appropriate chapter from an appropriate textbook and do practice problems. It takes experience and practiced eye. Algebra books have chapters on

38. Math: matrices

If A and B are both square n x n matrices, If AB = I, prove BA = I Presumably you have to do this without using the usual properties of the inverse of matrices. But we do need to use that if there exists a matrix B such that A B = I then the equation A X =

39. math

I'm trying to follow a research paper The paper shows an equation to minimize. That makes perfect sense. Then, the paper says: "The optimal solution to the least squares problem [above] is found by differentiation as a solution of a linear system of

40. math

integrate: (x^2 + 1)^k dx

41. math

limit (x -> 0): (cos x - 1) / x The answer is 0. I can see this with graphing calculator, but how do I solve algebraically?

42. math

There is one step in a proof that I don't understand. Could someone please explain? u = any vector in vector space S W = finite dimensional subspace of S with orthonormal basis of vectors {v1, v2, ..., vn} The theorem to prove is: u can be expressed

43. math

I'm having trouble understanding one step in a proof of the Cauchy-Schwarz inequality: u = a non-zero vector v = another vector a = (so a > 0 by positivity axiom) b = 2 c = (so c >= 0 by positivity axiom) t = any real number 0

44. math

Show that the formula for a line through two points (a1,b1) and (a2,b2) is: y=(b1-b2)/(a1-a2) * x + (a1*b2-a2*b1)/(a1-a2) The slope part looks right. Could someone explain how the y-intercept part makes sense? I would think that the y-intercept is:

1. Finite Math

3! = 3*2*1 = 12 Starting at A, he can go to B or C or D (three choices). From there, the driver has two choices. Then will have only one route left. That sounds like an easy version of the standard traveling sales person problem.

posted on March 2, 2009
2. math

Thanks guys. I wrote a simple computer program that verifies that S = 1/(1-x) holds when 0 < x < 1 (hence the series converges), but not when x > 1 (and the series diverges). That wasn't clear in the textbook. Thanks for the help.

posted on February 10, 2009
3. math

Ah ha! That's exactly what that is. And I knew that a long time ago. Thanks! It doesn't show up on Wikipedia's greek alphabet page at all, but that's more than good enough! Thanks!

posted on January 16, 2009
4. math

Thanks for the great suggestion Count. I ordered the third edition of that book from Amazon. The TOC looks great. Thanks!

posted on April 25, 2008
5. C++ Programming

That's code to walk through a linked list. I can't say the exact output because I can't see what the variable "list" is. Also, there are missing braces after the while statement. If the program is run without braces, and list is not null, the iteration

posted on April 19, 2008
6. Calculus

That's what I needed. Thanks so much for the help!

posted on March 7, 2008
7. statistics

Damon, that can't be right. As n approaches infinity, S^2 should approach sigma^2. Also, the wikipedia entry does use both sample size and population size in their formula which is one reason that I wanted to see it derived.

posted on February 21, 2008
8. statistics

I meant "expected" value, not "estimated" value. Sorry about that.

posted on February 21, 2008
9. math

Thanks so much for working that out. In hindsight, I did the problem right except that I made a mistake in calculating

posted on January 18, 2008
10. math

Thanks Count Iblis! I was mistakenly integrating with pi/2 instead of 2*pi and every time I redid the problem, I just remade the same mistake without noticing it. Your help pointed out the issue. Thanks so much!

posted on January 17, 2008
11. Calculus

Thank you bobpursley. My surface area integral was bad. I was incorrectly assuming S = Int 2*pi*f(x) dx I read through proof. It is S = Int 2*pi*f(x)*sqrt(1+(dy/dx)^2) dx Thanks!

posted on January 14, 2008
12. Calculus

That's probably close enough Damon. thanks!

posted on January 13, 2008
13. algebra

If a is large and b is small: First rule: a = 12 + b Second rule: b + 2a = 39 Solve those two equations for a. The answer is choice "c"

posted on January 10, 2008
14. Question

Wow! Thanks for answering and thanks again for all the valuable homework help!

posted on January 7, 2008
15. calculus

Thanks Reiny + Iblis! This is from Wiley textbook "Calculus: Early Transcendentals Combined, 8th Edition", section 8.4. I think problem #41 (from memory). I typed it right. The answer you two wrote matches the book, however I couldn't figure out how to do

posted on January 7, 2008
16. math

That doesn't look right. First, 36/5 = 7.2 (not 7.25) Secondly, you should do all multiplication first, then do subtraction. 9*4/5 - 4/5 7.2 - 0.8 = 6.4

posted on January 2, 2008
17. Math

The max is 31/6 (no other value is greater) The minimum is -3 (no other value is less)

posted on January 2, 2008
18. calculus

sorry. posted too quickly. got the answer. Via trig substitution answer comes to: ln|sqrt(x^2+4)/2| + c which is the same as the other answer

posted on December 31, 2007
19. calculus

of course. That makes perfect sense. Thanks!

posted on December 31, 2007
20. calculus

posted on December 31, 2007
21. calculus

Ack! Actually, I just typed that up wrong. I didn't make that mistake on paper. My answer is still coming up wrong. Thanks for helping drwls. sqrt(x^2 - 9) = 3 * tan t dx = 3 * sec t * tan t * dt The rest is the same: Integral simplifies to: sec t dt

posted on December 31, 2007
22. math

Nevermind. Found the solution: 1) Multiply by (csc x + cot x)/(csc x + cot x) 2) Substite u = csc x + cot x into integral 3) Comes out to -du/u 4) Integrates to -ln |u| + c 5) Equals -ln |csc x + cot x| + c

posted on December 17, 2007
23. calculus

makes perfect sense. Thanks Count!

posted on November 5, 2007
24. math

Thanks! Actually, the problem was printed in my textbook like that with the equation using the variable y, but with dx rather than dy. This seems to be a textbook error. I wasn't sure whether that was the case or whether I was doing something wrong.

posted on September 16, 2007
25. math

Thanks!

posted on September 16, 2007
26. math

16a - 5b - (-6a - 15b) - (-4b) = 16a - 5b + 6a + 15b + 4b = 22a + 14b

posted on September 16, 2007
27. Beginning Algebra

(2b^3)^3 * 3(b^-4)^2 step #1) = 8b^9 * 3b^-8 step #2) = 24b Explanation: step 1: (2^3 is 8, b^3^3 = b^9, b^-4^2 = b^-8) step 2: Multiply the coefficients (8*3=24). Muliply the b terms: b^9 * b^-8 = b^1 = b

posted on September 16, 2007
28. Math

The final answer is (x^2 + 5)(x^2 - 4) If you multiply that, you will get your original equation.

posted on September 4, 2007
29. Math

(x^2 + 5)(x^2 - 4) If you set y = x^2 and look at the original as: y^2 + y - 20 It should factor easily to (y + 5)(y - 4) which equals: (x^2 + 5)(x^2 - 4)

posted on September 4, 2007
30. math

Assuming there are 26 letters (no distinction among case) and 10 digits: A) 26 * 26 * 10 = 6760 B) 26 * 25 * 10 = 6500 C) 26 * 1 * 10 = 260

posted on September 4, 2007