Ask a New Question
Search
Questions and answers by
mathstudent
Questions (44)
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 =
4 answers
502 views
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
2 answers
611 views
I've finished studying a full textbook on linear algebra and another on statistics. I've done most of the practice problems and
2 answers
585 views
I'm trying to follow a research paper
The paper shows an equation to minimize. That makes perfect sense. Then, the paper says:
1 answer
602 views
Integrate e^(-x^2/2) dx
What branch of calculus is this? Is this differential equations?
2 answers
524 views
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
6 answers
1,197 views
Find the least squares approximation of x over the interval [0,1] by a polynomial of the form a + b*e^x
-------------------------
2 answers
846 views
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 + ...
2 answers
768 views
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
1 answer
707 views
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
3 answers
756 views
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,
2 answers
531 views
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
2 answers
883 views
Dear experts,
What is your motivation to provide all this help? I'm extremely grateful for this service, but why do you help so
6 answers
541 views
Integrate: dx/(2x^2 + 4x + 7)
3 answers
450 views
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 answer
646 views
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
2 answers
1,133 views
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 =
6 answers
841 views
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 +
2 answers
644 views
Integrate: csc x dx
1 answer
374 views
Find the arc length of
y = ln(cos x) over x = [0, pi/4]
1 answer
459 views
How do I derive the secant reduction formula? Am I asking this question wrong?
Integrate: (sec x)^n dx
1 answer
470 views
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 +
0 answers
727 views
integrate: (x^2 + 1)^k dx
1 answer
308 views
integrate: (x^2 + 1)^k dx
0 answers
319 views
How do I derive the integration reduction formula for tangent?
Integral of (tan x)^n dx = ... I can do the derivations for
2 answers
607 views
Integrate: (sin 2x)^3 dx
I can see the answer, but how do I do this?
2 answers
353 views
Integrate: y/sqrt(2y+1) dx
2 answers
2,102 views
Prove
limit as x approaches +infinity of (1 + 1/x)^x = e
1 answer
440 views
limit (x -> 0): (cos x - 1) / x
The answer is 0. I can see this with graphing calculator, but how do I solve algebraically?
1 answer
547 views
Prove that the trace is a similarity invariant.
In other words, if two matrices are similar, then they must have the same trace.
0 answers
735 views
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
0 answers
819 views
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'
0 answers
550 views
I'm having a little trouble understanding the difference between the codomain and the range of a function.
I'm reading the
0 answers
529 views
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
0 answers
697 views
Prove that if A is a diagonalizable matrix, then the rank of A is the number of nonzero eigenvalues of A.
http://ltcconline.net/g
0 answers
772 views
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:
0 answers
935 views
If A^TA is an invertible matrix, prove that the column vectors of A are linearly independent.
You know that if statement X
0 answers
1,289 views
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
0 answers
451 views
I'm having trouble understanding one step in a proof of the Cauchy-Schwarz inequality:
u = a non-zero vector v = another vector a
0 answers
615 views
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
0 answers
611 views
Prove that for all real values of a, b, t (theta):
(a * cos t + b * sin t)^2 <= a^2 + b^2 I will be happy to critique your work.
0 answers
784 views
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
1 answer
1,046 views
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
0 answers
457 views
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
0 answers
715 views
Answers (30)
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.
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.
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!
Thanks for the great suggestion Count. I ordered the third edition of that book from Amazon. The TOC looks great. Thanks!
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
That's what I needed. Thanks so much for the help!
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.
I meant "expected" value, not "estimated" value. Sorry about that.
Thanks so much for working that out. In hindsight, I did the problem right except that I made a mistake in calculating
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!
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!
That's probably close enough Damon. thanks!
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"
Wow! Thanks for answering and thanks again for all the valuable homework help!
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
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
The max is 31/6 (no other value is greater) The minimum is -3 (no other value is less)
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
of course. That makes perfect sense. Thanks!
thanks damon! I follow perfectly.
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
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
makes perfect sense. Thanks Count!
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.
Thanks!
16a - 5b - (-6a - 15b) - (-4b) = 16a - 5b + 6a + 15b + 4b = 22a + 14b
(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
The final answer is (x^2 + 5)(x^2 - 4) If you multiply that, you will get your original equation.
(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)
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
