# All Questions

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### Order of Rate of Growth

How would you put these functions in order of rate of growth from the greatest to the smallest? $f(x) = log_2 x$, $g(x) = x^x$, $h(x) = x^2$, $k(x) = 2^x$ I took the derivatives and ended up with ...
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### Evaluating limit (iterated sine function)

The limit is $$\lim_{x\rightarrow0} \frac{x-\sin_n(x)}{x^3},$$ where $\sin_n(x)$ is the $\sin(x)$ function composed with itself $n$ times: $$\sin_n(x) = \sin(\sin(\dots \sin(x)))$$ For $n=1$ the ...
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### Is the reimann zeta function exactly pi(x)

Where pi(x) calculates the number of primes less than or equal to a certain x value. The pnt (prime number theorem) x/logx or more accurately x/logx-1 has been the most popular method for ...
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### On singular points of parallels

Say $\gamma$ is a unit speed curve and its parallel is given by $$p (t) = \gamma (t) + d n(t)$$ where $n$ is the unit normal vector. I read that as $d$ varies the singular points of $p$ trace the ...
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### Rapid way to prove $[e_{ij},e_{lk}]=\delta_{jl}e_{ik}-\delta_{ki}e_{lj}$

Let $e_{ij}$ denote the $n\times n$ matrix with entries all zero but the $(i,j)$th one, in which we put $1$. Let then $\delta_{ij}$ be the Kronecker Delta. Finally $[A,B]:=AB-BA$ is the commutator ...
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### Let p be an odd prime number. Then show the following:

Let $p$ be prime, $p \geq 3$. Then show that $K_p$ is the union of $\frac{1}{2}(p-1)C_p$. I am once again at a loss for a starting point. Maybe just a small hint so I can work through this myself ...
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### Do Electrical Engineering Researchers Usually Know Higher Math? e.g. Measure and Distribution Theory, Functional Analysis

I am an EE undergraduate student, and I recently took two courses in signals and systems. We were exposed to things like the Dirac delta (without mention of distributions), Fourier series (without ...
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### Basic question related to dimension of intersection of two varities

Let $V$ and $W$ be irreducible varieties in $\mathbb{C}^n$. I have learned that intersection $V \cap W$ satisfies the following: $$codim \ V + codim \ W \geq codim \ V \cap W.$$ I was wondering if ...
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### On reparametrisation of curves (sorry for trivial question but I'm confused)

I'm confused about speed and reparametrisations of curves. To illustrate my confusion please let me elaborate using the simplest example I could think of: Let $\gamma : [0, 2 \pi ) \to \mathbb R^2$ ...
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### Consider the vector space V = {(a, 1 + a) | a ∈ R} with irregular definitions of addition and multiplication

with addition and scalar multiplication defined by (a, 1 + a) ⊕ (b, 1 + b) = (a + b, 1 + a + b) k '*' (a, 1 + a) = (ka, 1 + ka), k ∈ R find a basis for V. I started off with taking the general ...
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### Are there slight modifications to NP-complete problems which reduce them to P?

Recently I revisited the infinite harmonic series and its barely diverging sum, and how removing all the composite numbers from the sum still produces a divergent series (even more barely). In ...