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 .

42884 questions
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Solving an equation without product log function (Lambert's W function).

Let $x=1+y\log(x)$. How do we solve this equation for $x$? I know that $x$ can be represented in terms of the product log function (or the Lambert's W function) of $y$. My question is, can we solve it without the help of this product log function?…
nicole
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Is the function continuous at x=0?

Check if the function $f$ is continuous. $f(x)=$\begin{matrix} 0 & ,x=0\\ \frac{1}{[\frac{1}{x}]} & ,0
evinda
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are there $x_{1},x_{2} \in [0,2]$ such that $x_{1}-x_{2}=1$ and $f(x_{1})=f(x_{2})$?

Let $f$ continuous at $[0,2]$ with $f(0)=f(2)$.Check if there are $x_{1},x_{2} \in [0,2]$ such that $x_{1}-x_{2}=1$ and $f(x_{1})=f(x_{2})$ . How can I do this?
evinda
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2 answers

Why is the equation between these intervals true?

Can you show me why is the following true? $$ \left[a;b\right] =\bigcap_{n=1}^\infty \left]a-\frac 1n ;b\right]$$ And why is this wrong? $$ \left]a;b\right] =\bigcap_{n=1}^\infty \left]a-\frac…
Arch
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1 answer

Description of what Frame Theory is?

I would like to have an idea what is the field Frame Theory. Can anyone describe what this field is and what kind of problems will be considered in this topic. Thanks.
AmirHosein Sadeghimanesh
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2 answers

Periodic Function with no Minimum is Constant

Let $f: \mathbb R \rightarrow \mathbb R$ be a periodic function, which means that there is some positive $p$ such that $f(x)=f(x+p)$ for all $x$. Is it the case that, if there is no minimum such $p$, then the $f$ must be a constant function?
Nishant
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Bounding a Bilinear Map $||A(v,w)||\leq M||v||||w||$

In a normed vector space I know that for a linear map $L:E\rightarrow F$ that there exists an $M\in \mathbb{R}$ such that $\forall x\in E$ $||L(x)||\leq M||x||$. The proof is this is quite straightforward but I am unsure how to generalize to a…
Mael
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convergence of a sequence involving greatest integer function

$$a_n=\frac{1}{n}\left[n\beta\right]+n^2\beta^{n}$$where $0\lt\beta\lt1$ Now since $[n\beta]=n\beta- \{n\beta \}$, we have $$a_n=\beta-\frac{1}{n}\{n\beta\}+n^2\beta^{n}$$ $$\implies a_n-\beta=n^2\beta^{n}-\frac{1}{n}\{n\beta\}\lt n^2\beta^{n}$$.…
tattwamasi amrutam
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question about measure zero and integrals

I am confusing about a subtle point in the following question Let Q be a rectangle in $R^n$; let $f:Q-->R$ be a bounded function. Show that if $f$ vanishes except on a closed set $B$ of measure zero, then the integral of f over Q exists and equals…
Seth
  • 3,325
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1 answer

Differentiable manifold?

Let $f\colon \mathbb R^2 \to \mathbb R^3$ be defined by the formula $$ f(x,y)=(\sin x,e^y\cos x,xy). $$ Simultaneously $y \geq 0$ and $0 < x < 2\pi$. The question is whether $f$ is differentiable manifold or not? And why?
user114119
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All convergent sequences are bounded confusion

We proved that all convergent sequences are bounded. However, when proving the following: If $x_n$ converges to $x$ and $y_n$ converges to $y$, then $\dfrac{x_n}{y_n}$ converges to $\dfrac{x}{y}$, we use the fact that if a sequence $y_n$ converges…
Warz
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Why is the derivative of an (everywhere differentiable) function on the real line the limit of a sequence of continuous functions?

If a function $g$ on $\mathbf{R}$ is everywhere differentiable, why is $f=g'$ the limit of a pointwise convergent sequence of continuous functions $f_n$? More generally, does this also hold for any function $f$ on $\mathbf{R}$ possessing the…
Aubrey
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How prove this $u(x,y)\ge 0,(x,y)\in D$

let $$D=\{(x,y)|x^2+y^2<1\}$$ and $u(x,y)$ be second order continuous partial derivatives on $\overline{D}$, and $$\dfrac{\partial^2 u}{\partial x^2}+\dfrac{\partial^2 u}{\partial y^2}+\dfrac{\partial u}{\partial x}+\dfrac{\partial u}{\partial…
math110
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2 answers

Example of a sequence

How to find a sequence having the following properties: $\dfrac{A_n}{B_n} \to 0$, but $\dfrac{\log(A_n)}{\log(B_n)} \to 1$ as $n \to \infty$.
Eowyn
  • 253
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6 answers

Show that there is a subspace $J$.

Suppose that $f$ is differentiable on $[0, 1]$, with $f(0) = 0$ and $f'(x) \geq m > 0$ for each $x \in [0, 1]$. Show that there is a subspace $J \subseteq [0, 1]$, with length greater than or equal to $\frac{1}{2}$, so that $f(x) \geq \frac{m}{2}$…
evinda
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