## Is the complex derivative speed November 28    3

The first thing I was told about the real derivative is that it's "how fast the function is growing" at a given point. This interpretation wasn't addressed in my complex analysis classes. Can the complex derivative also be interpreted as "s

## Taking the derivative of $x^{\sin(e^x)}$ November 28    2

How am I suppose to take the derivative of $f(x)=x^{\sin(e^x)}$?What should I make $u$ equals?I tried to make $u=\sin(e^x)$ and $u=e^x$ but they didn't work.Hint: Here, you want to (start off) by using logarithmic differentiation - that is, take the

## Palindrome Induction Proof November 28    1

Consider strings made up only of the characters $0$ and $1$; these are binary strings. A binary palindrome is a palindrome that is also a binary string.(a)Let $f(n)$ be the number of binary palindromes of length $2n$, for $n\ge 0$. Discover a formula

## Prove that in a bit string, the string 01 occurs at most one more time than the string 10. November 28    1

Good morning. This is my first question in a StackExchange forum. Let me know if I'm doing anything incorrectly (posting in the wrong forum, etc.).Prove that in a bit string, the string 01 occurs at most one more time than the string 10.I wish to use

## Prove by induction on strings November 28    1

I have this question: Prove by induction on strings that for any binary string w, (oc(w))^R = oc(w^R). note: if w is a string in {1,0}*, the one's complement of w, oc(w) is the unique string, of the same length as w, that has a zero wherever w has a

## Prove reversal of a string by induction November 28    1

I am trying to prove that:(uv)R = vRuRwhere R is the reversal of a String defined recursively as:aR = a (wa)R = awRI think I have the base case right, but I am having trouble with the inductive step and final proof.here is what I have:Base Stepprove

## Inductive Definition on the set of strings November 28    1

Given:$$\Sigma = \{ a, b, c \}.$$I am trying to give the inductive definitions of both the set of strings $\Sigma^*$ and $\Sigma^+$.Thank you.The set $\Sigma^*$ contains all strings. The set $\Sigma^+$ contains all non-empty strings.Your inductive

I'm trying to solve the following problem:Two players conduct simultaneously and independently a sequence of Bernoulli trials. Both have a probability $p$ for success in each Bernoulli trail. What is the probability that the first player will have $i ## Example of analytic piecewise-defined function November 28 2 Does there exist an analytic everywhere, piecewise-defined function$f$such that:$f(x) = g(x)$for$x < k$$f(x) = h(x) for x>k$$f(x) = r$for$x=k$With$g \ne h $($g$not the same function as$h$)If it exists, what is such an example?If$g$and ## lim sup and lim infs of Brownian Motion November 28 Below is my question. Q7.9 is what I'm stuck on. I've done Q7.8; I included it in the picture because I'll use it in Q7.9, and it gives a definition that I'll use.What I've done so far is th ... ## Piecewise monotonicity of real analytic functions November 28 This may have a completely trivial answer, but I don't see it at the moment:If the series expansion$f(x)=\sum_n a_n x^n$is valid on the whole of$\mathbb{R}\$, must there exist a countably infinite partition \ldots r_{-2} < r_{-1} < r_0 < r_1 ## Two way partitioning SDP with log barrier Newton step November 28 I'm trying to solve the Two way partitioning problem\begin{align*}&\text{maximize}&&x^TWx\\&\text{subject to}&&x_i^2=1,\quad i=1,\cdots,n\end{align*}The Lagrangian dual of above function is\begin{align*}&\text{maximize}& ## Can we check a range if some values fall in a range if have the some of values November 28 I have a set of natural numbers.Is there a way to check out whether all the numbers fall in a range, say from 10 to 20, by looking at their sum.Or is their any such property of a range which helps us to identify it?Where I am coming from :I just had ## Coordinate Geometry:Locus Based Problem November 28 1 A rod AB of length l slides with its ends on the coordinate axes.Let O be the origin.The rectangle OAPB is completed. How to prove the locus of the foot of perpendicular drawn from P onto AB is x^{2/3}+y^{2/3}=l^{2/3}  ?Let N(x,y) be the foot of ## Parameters to represent degrees of freedom in n\times n orthogonal real matrices November 28 1 An n\times n orthogonal real matrix A is a set {A_{ij}} of n^2 real numbers that satisfy the constraints:\sum_k A_{ik} A_{kj} = \delta_{ij} $$for all 1\leq i,j\leq n. The equations (1.) represent$$ n + \binom{n}{2} = \frac{n(n+1)}{2} $$## Regular local ring resultreference request November 28 1 Reference needed for the following result: Let R be a regular local ring with maximal ideal \mathfrak m. If A is a flat R-algebra and A/(\mathfrak m) is a domain, then A is a domain. This is not true: consider A=R\times K where K is t ## Reference on Geometric Topology November 28 4 Geometric topology is more motivated by objects it wants to prove theorems about. Geometric topology is very much motivated by low-dimensional phenomena -- and the very notion of low-dimensional phenomena being special is due to the existence of a bi ## \mathbb{R}P^3 is homeomorphic to the lens space L(2,1) November 28 2 Show that the 3-dimensional real projective space \mathbb{R}P^3 is homeomorphic to the lens space L(2,1). (I am not sure but the problem is probably from the book Knots and Links which is written by Rolfsen.)In addition to explicitly identifyin You Might Also Like • Here is an example:24.30 + 66.6% = 40.50 40.50 - 60% = 24.30 or (24.30 + 66.6%) - 60% = 24.30 I know if I ad ... • Prove that \prod_{k=1}^{\lfloor (n-1)/2 \rfloor}\tan \left(\frac{k \pi}{n}\right)= \left\{ ... • Well, my question is essentially:Let R be a Factorial Ring (UFD, basically) and let p be a prime element ... • I have following problem. Let assume that lifespan in the population has normal distribution with certain me ... • Is there any way to count the number of distinct combinations of a set of objects where some objects may be ... • The wikipedia article on linear least squares only considers overdetermined systems (rows \geq columns). I ... • reduction order method xy''-(1+x)y'+y=x^2e^{2x}, being y_1=1+x a solution of the homogeneous equation.I ... • Here is a fun integral I am trying to evaluate:$$\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \ dx=\frac{\pi \b ...
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