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
1
vote
1 answer

How find the $\frac{1}{e}\le R\le 1$

Qustion: let $a_{n}> 0$,and such $\displaystyle\sum_{n=1}^{\infty}a_{n}$ converge,let $$b_{m}=\sum_{n=1}^{\infty}\left(1+\dfrac{1}{n^m}\right)^na_{n}$$. show that $$\dfrac{1}{e}\le R\le 1$$ where the $R$ is the radius of convergence of…
math110
  • 93,304
1
vote
1 answer

How prove this $\overrightarrow{r_{i}}\cdot\overrightarrow{r_{j}}\ge\frac{1}{2}$

let $a,b,c$ are real numbers,and such $a+b+c=0,a^2+b^2+c^2=1$, we define: $\overrightarrow{r}=(x_{i},y_{i},z_{i})(i=1,2,3,4,5,6)$,where $\{x_{i},y_{i},z_{i}\}=\{a,b,c\}$, show that: there are exst…
math110
  • 93,304
1
vote
2 answers

If $N$ is a complete linear subspace of $H$ and $\inf_{f \in N} |f-g| = d$, prove that $\exists f'$ such that $f' \in N$ and $|f'-g|=d$

The problem as stated is Let $H$ be a Hilbert space. If $N$ is a complete linear subspace of $H$ and $\inf_{f \in N} |f-g| = d$, prove that $\exists f'$ such that $f' \in N$ and $|f'-g|=d$. I would like to try to prove that there exists a Cauchy…
Pricklebush Tickletush
  • 344
1
vote
2 answers

Prove that lim is 0.

Prove that $$\lim_{x\to0}\sqrt{|x|}\sin\left(\frac1x+x^{10}\right)=0.$$ How do I show in a rigorous way that this limit as $x\to 0$ equals $0$ ? Any tips or suggestions would be great!
Dafty
  • 509
1
vote
4 answers

Prove that if all the vertices of a graph have degree 3, then the graph must have a cycle

Hello can you help me to prove this. The hint for the problem is: Think of what it means for a graph to have no cycles. So I believe this will be a contrapositive proof, but still could not do it.
AS8x
  • 11
1
vote
1 answer

Prove C[0, 1] is complete with metric a different metric

would any one tell me whether C[0,1] is complete under the following metric $$ \sup_{t\in [0, T]}e^{-Lt}|x(t)-y(t)| $$ and how to prove the claim I know some reasoning on how to prove C[0, 1] is complete with the usual sup norm. Just wondering…
123
  • 11
1
vote
3 answers

A little help with point set topology

Can anyone give me an EXAMPLE of adherent point that is not an accumulation point or just opposite.
S L
  • 11,731
1
vote
1 answer

inf A of $n^22^{-n}$

Let $A=\{n^22^{-n}, n \in \mathbb{N}\}$. Find $\inf A$, $\sup A$. I tried starting by proving that $\frac{n^2}{2^n} \leq 1/n$ by induction. After, I showed that $\frac{n^2}{2^n} \geq 0$. By the squeeze theorem, $$0 \geq \frac{n^2}{2^n} \geq…
Justin D.
  • 745
1
vote
1 answer

Prove$ f(x, y)=\dfrac{x}{y}$ is continuous using continuity definition

How to prove $f(x, y)=\dfrac{x}{y}$ ($y$ is not $0$) is continuous using continuity definition? couldn't figure out how to define delta...
user99051
  • 11
1
vote
3 answers

Does $\lim_{n\rightarrow \infty } {\left| a_n \right|} = {\left| L \right|} $ hold for$ L \neq 0$?

I have this question: Prove that $\large \lim_{n\rightarrow \infty } {a_n} = L \iff \lim_{n\rightarrow \infty} {\left| a_n \right|} = |L|$ when $L = 0.$ Does that hold for L $\neq 0$ ? Well, I approached this problem by saying: take $\large…
Logarithm
  • 385
1
vote
0 answers

Attributes of values over time for Bayes classifier

I'm measuring acceleration over time. I want to collect a bunch of attributes of the measured values. Example, mean, max, min, standard deviation, time between peaks, etc. I'm not a math person and don't know what to look for to find out more…
user98111
  • 11
1
vote
1 answer

On compositions $g \circ f$ and whether $f$ is surjective

\begin{align} f: X \longrightarrow Y \\ g: Y \longrightarrow Z \\ g \circ f: X \longrightarrow Z \tag{is bijective} \end{align} The bijective conditions only applies to $ g \circ f$. I already managed to show that in this case $f$ must be injective…
Spaced
  • 3,499
1
vote
3 answers

convergence of a sequence (partial fractions)

Let's define {${x_n}$} as $x_1=0.1, x_2=0.101, x_3=0.101001,....$ . Then we need to find out if the sequence convergences or not and the limit. This is how i proceeded. $x_1=\frac{1}{10}, x_2=\frac{1}{10}+\frac{1}{1000},…
tattwamasi amrutam
  • 12,802
  • 5
  • 38
  • 73
1
vote
1 answer

Can I say $f$ is differentiable at $c$ if $D_u(c) = \nabla f(c) \cdot u$ for all unit vectors $u$?

Can I say $f$ is differentiable at $c$ if $D_u(c) = \nabla f(c) \cdot u$ for all unit vectors $u$? I think I can because it guarantees a tangent plane. But I don't know how to prove this precisely. Anyone can give an advice or a proof? Thanks.
Analysis
  • 877
1 2 3
…
99 100