showing

1. Showing there is a dense set of singular points when |z| = 1 for a power series

I've been stuck on a complex analysis problem with showing there is a dense set of singular points for the power series \sum_{n=0}^{\infty} z^{2^n} I'm guessing I should use the rationals, but I really don't know where to go beyond there. I can parametrize the unit circle with e^{2\pi i\theta}...
2. Showing that there is no simple group of order 6p^r

Show that there is no simple group of order 6p^r for any prime p and positive integer m.
3. Verify that the functions are inverse by showing that f o g and g o f

are the identity function. f(x)=5x and g(x)=1/5x f(g) 5x(1/5x)= x^2 g(f) 1/5x(5x)= x^2 Did I do this right, where did I mess up if I did this wrong? I am pretty sure they are suppose to both = x if they are identity functions. ( the answers are not shown in my book). Thank you.
4. Kernel method- showing kernel is valid

How to show that the following kernel is [valid][1]? $K(x,y) = \frac1{1-xy}$, where $x, y$ are in $[-1,1]$. Can someone help and possibly provide reasonable explanation? Also by giving any distinct input $x(1),...,x(m)$ how can we show that it is invertible?
5. Help Needed Showing Work

I needed help showing work for these two. Thanks for the help.
6. showing a homothetic utility function is linear in income

A homothetic function is one which is a monotonic transformation of a homogeneous utility function. I am asked to show that if a utility function is homothetic then the associated demand functions are linear in income. in general if H is homothetic and we compose it with a function g which is...
7. Showing an integral domain is PID

Let R be an integral domain and suppose every prime ideal in R is principal. Assuming the set of non-principal ideals is non-empty I used Zorns Lemma to show that it will have a maximal element under inclusion. Call this element I that is an ideal such that is is maximal with regards to being...
8. Find the slope of a curved line showing population growth

There is an example in the online calculus course I'm taking that shows a graph which shows y=population and x=number of years. In the example it shows a point which represents the population at that time. So at point "A" the year was 1985 and the population was 3600. Then is says the slope of...
9. Showing each side is a subset of the other side

I am asked to show that each side is a subset of the other side, but the book's answer is sort of long and hard to understand. Is there another alternative answer that is much shorter and easier to understand? The venn diagram is there just to help me visualize.
10. Problem showing a set of polynomials is a basis for P2

I can't figure out to solve this problem for a polynomial.
11. Showing a sequence is monotonic decreasing by induction

$a_n=\frac{n^2}{2^n}$ Let $P(n)$ be $a_{n+1}<a_n$ for $n>3$. Then $P(1)=\frac{4^2}{2^4}<\frac{3^2}{2^3}$ is true. Assume $P(k)$ is true and show $P(k+1)$ is true. Here I'm getting stuck quickly. I'd like to find some quantity I can add to the statement $P(k)$ but ultimately the quantities...
12. Showing regular languages are closed under min using DFA's

Hello all! I think I've got the idea of this question, but am not sure how to create its DFA's: Question: Using DFA’s (not any equivalent notation) show that the Regular Languages are closed under Min, where Min(L) = {w | w ∈ L, but no proper prefix of w is in L}. This means that w ∈ Min(L) iff...
13. Showing the modified Dirichlet function is discontinuous

Show, using the $\epsilon-\delta$ definition of continuity, that the modified Dirichlet function, i.e., $f(x) = x$ if $x$ is rational and $f(x) = 0$ if $x$ is irrational, is discontinuous at all points $c \neq 0$ My attempt: Is the following argument right (using the sequential definition of...
14. Showing that a set spans the subspace of symmetric matrices

I'm not really sure how to show this. It's the part about symmetric matrices that throws me off. What I know: A symmetric matrix has the property that A = A^T. To show that the set spans, I could create a matrix and show that if there are leading ones in each row, without a pivot in the...
15. Showing a compuond proposition is a tautology using logical equivalences

Hi all, I am currently working on showing that [p AND (p IMPLIES q)] IMPLIES q is a tautology and, really just don't know where to begin. Not expecting any answers, but to be pointed in the correct direction.
16. Showing that a number is rational/irrational

I have a bunch of questions that I don't know how to approach about whether a number is rational or irrational Could someone give me an idea of how to approach questions like the following: 1 + srt(2) + srt(3/2) Is this rational or irrational (and why)? thanks :)
17. Showing that f is the potential function of F

Hey guys. I'm trying to solve an exercise, and the solution is proberbly simpler than what I'm trying to do. We are given F = (x^2 + y^2)^{-1} \binom{-y}{x} The curve C is given by the parametrization \mathbf{r}(t) = (r(t)\cos(\theta (t)) , r(t) \sin (\theta (t))) where r and \theta both...
18. Showing CFG is ambiguous

To show it i need to find a string belonging to language and show that has 2 different parsin trees. Is there way to tell which string could possibly have 2 diff trees or do i have to generate like 20 strings belonging to language and test each string? I would much appreciate ideas how to do...
19. Showing the bibliographic or... entry in a popup when you hover over the citation key

Hi. I neeed a file tex for Showing the bibliographic or... entry in a popup when you hover over the citation key. I know we can use fancytooltips package, but I don't how! please attach tex. Thanks a lot.
20. Showing a matrix is not diagonalizable

The matrix is B= 3 -1 1 5 and I hate to show that it's not diagonalizable . I'm not really sure where to begin. I think the determinant (which I know equals 16) has something to do with it but I'm not sue where to go from there. I also need to reverse the rows of B and find both the...