Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [analysis]

Mathematical analysis. Consider a more specific tag instead: (real-analysis), (complex-analysis), (functional-analysis), (fourier-analysis), (measure-theory), (calculus-of-variations), etc. For data analysis, use (data-analysis).

Mathematical analysis is the rigorous version of calculus. In fact, it investigates the theorems in calculus with enough care and deals with them more deeply, trying to generalize the ideas in calculus. You can consider a more specific tag instead: , , , , , , etc. For data analysis, use .

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Polygons circumscribed to a circle with the smallest circumference

Let $n \geq 3$. Prove that among all $n$-polygons circumscribed to a (particular) circle, the regular $n$-polygon has the smallest circumference. It shouldn't be difficult, but I don't even know how to start.
Jules
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Supremum, and an increasing function

let $f(x)$ be an incresing function, and let $C$ be a constant s.t. $f(x) \leq C.$ Put $D = $ sup $f(x)$, and i need to show that $f(x) \rightarrow D$ as $x \rightarrow \infty$. It seems 'obvious' when i draw a picture, but hints for a formal proof…
Tom
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Can someone explain Sensitivity Analysis to a computer programmer

There are lots of long texts about Sensitivity Analysis but as a programmer I get easily bored or can't understand it. Can someone briefly explain Sensitivity Analysis to a programmer? Thanks.
ramazan polat
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Convolution of two heaviside functions

how can i find convolution of two heaviside functions centered at 1/2 and -1/2. I have tried to find the corresponding integral, but i stack due the centers are different.
Alemu
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Showing a Cauchy sequence does not have a limit

Okay basically I've managed to work through parts 1 a and b (with some help) now I'm a little stuck on part c). I think I can show fn is a cauchy sequence by virtue of the fact that fn-f tends to 0, but I'm stumped as to how I can then prove it…
user114612
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Applying theorems on differential functions

question http://s30.postimg.org/6jnj4ie75/Untitled.png I'm thinking that I need to do a proof by counter example? Is it possible to use Rolle's theorem: f is cts on [a,b] and differentiable on (a,b) and f(a)=f(b), so there exists a c in (a,b) such…
user127700
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Prove that if $\{a_n\}$ converges to $a$ and $|a| < 1$, then $\{a_n^n\}$ converges to 0

Prove that if $\{a_n\}$ converges to $a$ and $|a| < 1$, then $\{(a_n)^n\}$ converges to 0. This is what I have currently done. Please let me know if there is something wrong or if there is any other advice that you could provide to help me finish…
Raghu
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Characterisation of the limit superior and limit inferior

in my notes (University 1st year Analysis) is the following proposition : ! with the proof ! I don't understand what it means for the set to be finite/infinite and I am therefore a little hazy with the steps in the proof. Any…
user127700
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prove, $\int_0^x \left (\sum_{n=0}^\infty a_nt^n \right ) \ dt = \sum_{n=0}^\infty a_n \frac{x^{n+1}}{n+1}$

Let $\displaystyle \sum_{n=2}^\infty a_nx^n$ be a power series with radius of convergence $R>0$ prove, $\displaystyle \int_0^x \left (\sum_{n=0}^\infty a_nt^n \right ) \ dt = \sum_{n=0}^\infty a_n \dfrac{x^{n+1}}{n+1} $ The question gives a hint to…
Warz
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Open cover of $\mathbb{Q} \cap [0,1]$

Let $\alpha \in [0,1]$ such that $\alpha$ is irrational. Then an open cover of $\mathbb{Q} \cap [0,1]$ is $\{-1,\alpha-\frac{1}{n} \big | n \in \mathbb{N} \} \cup (\alpha,2)$. I found this solution and am a bit skeptical of it. How can we be sure…
user7090
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Determine if it is countable or uncountable

Determine if it is countable or uncountable The set $E$ of all circle in $R$$^2$ with centers at rational coordinate points and positive rational radius. I have no idea about this type of question.
user109403
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Intermediate Value Theorem application

I am trying to solve: Let $f:[a,b] \to [c,d]$ be a continuous bijection. Suppose $f(a) < f(b)$ (i) Let $a < x_1 < b$. Prove $f(a) < f(x_1) < f(b)$ (ii) Let $a < x_1 < x_2 < b$. Prove $f(x_1) < f(x_2)$ I think I need to use the IVT for this. For (i)…
user127700
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how to find the solutions of this equation (with Lambert Function)?

I need the solutions $x$, such that $x\ln|x|+\frac{1}{4}=0 $ is true. Wolframalpha gives http://www.wolframalpha.com/input/?i=xln|x|%2B1%2F4%3D0, but I never heard of the Lambert W-Function before. Can you give me a hint how to find the solutions of…
user98225
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Real and complex series question

Let $\sum a_n$ be a series of positive real numbers, n going from 0 to $\infty$, such that the series DOES NOT converge. Let $\left\{z_n\right\}$, $n\geq 0$ be a sequence of complex numbers. Form an associated sequence $\left\{w_n\right\}$ where…
user130113
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Show that $e^{f(x)}$ is Riemann Integrable

Suppose that $f:\mathbb{R} \to \mathbb{R}$ is Riemann Integrable and $f = 0$ for $f \notin [a,b]$. Show that $e^{f(x)}*\chi_{[a,b]}$ is Riemann Integrable. I think this means that: $g(x) = e^{f(x)} = e^{f(x)} $for$ a \leq x \leq b$ and $0$…
yhu
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