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,

    asked on January 18, 2008
  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

    asked on November 7, 2007
  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

    asked on January 14, 2008
  4. math

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

    asked on November 8, 2007
  5. math

    Prove that if A is a symmetric n x n matrix, then A has a set of n orthonormal eigenvectors. I've read the entire page and while it's on the correct topic, it doesn't prove what

    asked on January 19, 2007
  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?

    asked on December 15, 2006
  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

    asked on February 21, 2008
  8. calculus

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

    asked on January 6, 2008
  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

    asked on January 8, 2007
  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,

    asked on January 16, 2008
  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!

    asked on January 7, 2008
  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?

    asked on December 31, 2007
  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)

    asked on July 20, 2007
  14. math

    Prove that if A is a diagonalizable matrix, then the rank of A is the number of nonzero eigenvalues of A. I've read the entire page and while it's on the correct topic, it

    asked on January 19, 2007
  15. math

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

    asked on December 19, 2006
  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

    asked on April 25, 2008
  17. math

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

    asked on September 15, 2007
  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

    asked on July 20, 2007
  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

    asked on June 9, 2007
  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

    asked on January 13, 2008
  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:

    asked on January 13, 2008
  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

    asked on January 2, 2008
  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

    asked on December 31, 2007
  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

    asked on December 31, 2007
  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

    asked on January 13, 2007
  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

    asked on February 10, 2009
  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?

    asked on January 10, 2008
  28. math

    Integrate: csc x dx

    asked on December 17, 2007
  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!

    asked on November 5, 2007
  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?

    asked on January 16, 2009
  31. Calculus

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

    asked on March 7, 2008
  32. math

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

    asked on December 3, 2007
  33. Calculus

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

    asked on November 6, 2007
  34. math

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

    asked on September 15, 2007
  35. math

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

    asked on September 8, 2007
  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

    asked on January 26, 2007
  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

    asked on January 2, 2007
  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 =

    asked on December 4, 2006
  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

    asked on April 18, 2008
  40. math

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

    asked on November 7, 2007
  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?

    asked on September 4, 2007
  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

    asked on January 5, 2007
  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

    asked on January 4, 2007
  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:

    asked on December 6, 2006
  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

    thanks damon! I follow perfectly.

    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


    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