mathstudent
Most popular questions and responses by mathstudent
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 
math
How do I derive the secant reduction rule? Integral (sec x)^n dx = Integral (sec x)^(n2) * (sec x)^2 dx = Integral ((tan x)^2 + 1)^(n/21) * (sec x)^2 dx Doing a substitution with: u = tax x du = (sec x)^2 dx = Integral (u^2 + 1)^(n/21) * du At this
asked on November 7, 2007 
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 usubstitution, integration by parts, partial
asked on January 14, 2008 
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 
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
asked on January 19, 2007 
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 
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 
calculus
Integrate: dx/(2x^2 + 4x + 7)
asked on January 6, 2008 
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 
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 
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 
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 
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 
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
asked on January 19, 2007 
math
Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2
asked on December 19, 2006 
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 
math
Integrate: y/sqrt(2y+1) dx
asked on September 15, 2007 
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 
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 
Calculus
Suppose that the region between the xaxis and the curve y=e^x for x>=0 has been revolved around the xaxis. 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 
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 TI89 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 
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 
calculus
Integrate: dx/sqrt(x^29) 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: lnsec
asked on December 31, 2007 
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 
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 
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/(1x) 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 
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 
math
Integrate: csc x dx
asked on December 17, 2007 
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 
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 
Calculus
Integrate e^(x^2/2) dx What branch of calculus is this? Is this differential equations?
asked on March 7, 2008 
math
Find the arc length of y = ln(cos x) over x = [0, pi/4]
asked on December 3, 2007 
Calculus
integrate: (x^2 + 1)^k dx
asked on November 6, 2007 
math
Integrate: (sin 2x)^3 dx I can see the answer, but how do I do this?
asked on September 15, 2007 
math
Prove limit as x approaches +infinity of (1 + 1/x)^x = e
asked on September 8, 2007 
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 
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 
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 
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 
math
integrate: (x^2 + 1)^k dx
asked on November 7, 2007 
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 
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 
math
I'm having trouble understanding one step in a proof of the CauchySchwarz inequality: u = a nonzero 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 
math
Show that the formula for a line through two points (a1,b1) and (a2,b2) is: y=(b1b2)/(a1a2) * x + (a1*b2a2*b1)/(a1a2) The slope part looks right. Could someone explain how the yintercept part makes sense? I would think that the yintercept is:
asked on December 6, 2006

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 
math
Thanks guys. I wrote a simple computer program that verifies that S = 1/(1x) 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 
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 
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 
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 
Calculus
That's what I needed. Thanks so much for the help!
posted on March 7, 2008 
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 
statistics
I meant "expected" value, not "estimated" value. Sorry about that.
posted on February 21, 2008 
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 
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 
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 
Calculus
That's probably close enough Damon. thanks!
posted on January 13, 2008 
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 
Question
Wow! Thanks for answering and thanks again for all the valuable homework help!
posted on January 7, 2008 
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 
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 
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 
calculus
sorry. posted too quickly. got the answer. Via trig substitution answer comes to: lnsqrt(x^2+4)/2 + c which is the same as the other answer
posted on December 31, 2007 
calculus
of course. That makes perfect sense. Thanks!
posted on December 31, 2007 
calculus
thanks damon! I follow perfectly.
posted on December 31, 2007 
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 
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 
calculus
makes perfect sense. Thanks Count!
posted on November 5, 2007 
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 
math
Thanks!
posted on September 16, 2007 
math
16a  5b  (6a  15b)  (4b) = 16a  5b + 6a + 15b + 4b = 22a + 14b
posted on September 16, 2007 
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 
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 
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 
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