# product

1. ### domain of combined function

Hi, I hope someone can help. I'm trying to figure out the domain for the product of f(x) and g(x). f(x) = \log_{10}(x+3)^2 g(x) = \sqrt{x-1} I know that the domain for f(x) is x > -3 and the domain for g(x) is x \leq -1 or x \geq 1. According to my textbook the domain for the product of...
2. ### The Marginal Revenue

For the equations below, q is the total number of units produced per day by m employees of a manufacturer, and p is the price per unit at which the q units are sold. Find the marginal-revenue product for the given value of m. q = (500m - m^2)/50, p = -0.3q + 90; m = 70
3. ### Linear Algebra: help with inner product space

I don't understand how to solve this type of problems and I can't find solved examples anywhere in my textbook or the internet. Can you help me out? In R^3 it's given the symmetric, bilinear form F: R^{3}\times R^{3}\rightarrow R : F((x_{1},y_{1},z_{1}),(x_{2},y_{2},z_{2})) = 3...
4. ### Getting the result of this dot product

Hello Guys, I am having trouble with this algebra. I don't know how to get v dot w = 1/2(x+y+z)^2 - 1/2(x^2+y^2+z^2) I tried (x+y+z)(x+y+z) and ended with x^2+y^2+z^2 + 2xy+2zx + 2zy I separated them and took out 1/2(xy+zx+zy) after this I'm completely stuck.
5. ### vector product and vector sum

what is the vector sum of (2,10,-50) and (30,-4,0) and also explain the definition of vector sum and vector product.vector
6. ### epsilon delta product limits

can you multiply two functions with each function approaching different x values----Example (x+4)=L as x approaches 2-----------(x+7)=M as x approaches 3? The Theorem states limit as X approaches a (f(x)g(x)=LM---I'm assuming both functions would have to approach the same a value? Thanks Delbert
7. ### Tensor Products of Modules and Free Abelian Groups based on Cartesian Product

I am reading Donald S. Passmore's book "A Course in Ring Theory" ... I am currently focussed on Chapter 9 Tensor Products ... ... I need help in order to get a full understanding of the free abelian group involved in the construction of the tensor product ... ... The text by Passmore...
8. ### Vector algebra and dot product

Again another relatively simple question. This one is part of a larger question that i can do but its just this simple part that is confusing me. Consider a unit vector ˆu, an arbitrary vector v, and a vector w which is the reflection ofv in a line in the direction of ˆu.(a) Show that w = 2 (ˆu...
9. ### Trig Product and Sum Help

Hi I am struggling with the following question. The instantaneous power, p, in an electric circuit is given by p = iv,where v is the voltage and i is the current. Calculate the maximum value of power in the circuit if v = 0.02\sin (100\pi t) volts i = 0.6\sin (100\pi t + \frac{\pi}{4} )...
10. ### Prove using Product to sum identities

Prove Cos (α – β) = cos α cos β + sin α sin β Hint:Keep the left side as is and use the Product to Sum Identities. Then, distribution to simplify the right side. I could really use some help on this..
11. ### Proof of inner product relation in a Hilbert space

Hello everyone I have been given a task where I need to prove, \forall \textbf{v} \in H, the following formula: <\textbf{v},\sum \limits^{\infty}_{k=1}c_k \textbf{v}_k>=\sum \limits^{\infty}_{k=1}\bar{c_k}<\textbf{v}_k, \textbf{v} > Where < \: \cdot \: , \: \cdot \: > is an inner product...
12. ### Product of Vectors

Hi Members, I want to prove the following(1)$(\vec{a}-\vec{b}) X (\vec{a}+\vec{b})=2\vec{a} X \vec{b}$ (2)$\vec{a} X (\vec{b} + \vec{c}) + \vec{b} X (\vec{c} + \vec{a}) + \vec{c} X (\vec{a} + \vec{b}) = 0$ (3) [i j k]=1 I have proved the first two identities by solving the following...
13. ### Cholesky decomposition of kronecker product

Hi, Is there any proof that cholesky(A\otimes B)=cholesky(A)\otimes cholesky(B) for A and B symmetric? It seems correct for 2\times 2-matrices, but is it in general?
14. ### Composition series for direct product (groups).

Hi: Let G= H1 x H2 for some simple groups H1, H2. I want to construct a composition series for G. I suspect that G >= 1 x H2 >= 1 x 1 is a such a series. To prove it, I begin by assuming 1 x H2 is normal in L and L is normal in G. Then it is enough to prove that either L = G or L = 1 x H2. If...
15. ### Finding the derivative using the product and quotient rules.

Hi, I am trying to solve a problem that asks for the derivative by using values from a given table. It is one of MathXL's practice problems, and after getting it wrong the answer of \frac{71}{9} was provided. I have been unable to figure out how they came to that conclusion using the product...
16. ### Logarithm Rule in integral problem (Product)

Is this how you would implement the logarithm rule for product? If it is then the answer would be 0, which I highly doubt since the original problem is taking the volume of a shaded region revolved about the x axis.
17. ### Product Rule Proof

Hi Everyone, So I decided to look up the proof for the Product Rule since I always use it, but I want to know why it makes sense. I came across this great webpage: Pauls Online Notes : Calculus I - Proof of Various Derivative Properties So here are my specific questions: 1. What you are...
18. ### Cross Product

- the problem The matrix problem below: Below is an example problem:
19. ### cross product - 3

= a X b ?? b X a ? b X a = ??

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