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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Why a number/infinitesimal is equal to infinity?

Why a number/infinitesimal+ is equal to infinity? Why a number/infinitesimal- is equal to -infinity? If a real number is 5, and a infinitesimal positive is 0+, is 0.1 for example, no? I got this doubt while I was doing a limit: $$\lim_{x \to…
user817101
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Could someone explain what a starlike function is?

Basically I'm looking for a way to describe shapes I'm working with in a graphics analysis program and I would like to know if what I'm working with are "starlike" shapes, as in, is the boundary a starlike function. The shapes I'm working with have…
user668074
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Reversal Point and Tangent line

Given is the function $\frac{1}{4}x^4-x^3+2x$, the task is to find the the turning points and then the tangent line to the left-most turning point. Deriving the functin we get $x^3 -3x^2 + 2x$ and with $x^3 -3x^2 + 2x = (x-1)(x^2-2x-2)$ the…
user66280
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Solving an equation to find a function

I am trying to solve the following equation and find a real-valued function $y\left(x\right)$ which satisfies $$ \exp{y\left(x\right)} + y\left(x\right) + 1 = 0, \hspace{0.2cm}\forall x>0 $$ Any ideas?
George
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Prove that ${(−1)^n}$ does not converge.

Prove that the sequence ${(−1)^n}$ does not converge. I know how to prove that the sequence diverges by contradiction, supposing the sequence converges to L. Then choosing $ε = 1$ such that $|(-1)^n - L| < 1$. Noting $|(-1)^{2n} -…
Sam
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Prove that if $({a_n} )$ is a sequence with two convergent subsequences $\{a_{n_k}\}$ and $\{a_{m_k}\}$

Prove that if $({a_n} )$ is a sequence with two convergent subsequences $\{a_{n_k}\}$ and $\{a_{m_k}\}$ such that $\lim_{k\to\infty}\{a_{n_k}\} \neq \lim_{k\to\infty}\{a_{m_k}\}$, then $({a_n})$ does not converge. I am not sure if I am…
Sam
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Set of Pythagorean Identities and The Golden Ratio.

Using Degrees Where A intercepts C the Y coordinate is Phi The X coordinate is (sin^-1(1/ phi^2))/ 2 Where B intercepts C the Y coordinate is 1/Phi The X coordinate is (sin^-1(1/phi) )/ 2 I got these equations while messing around with…
PythonGOD
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Prove that for a subsequence of natural numbers ${n_k}$, $k ≤ n_k$.

Prove that for a subsequence of natural numbers ${n_k}$, $k ≤ n_k$. I know I have to prove it using induction. I don't know if I'm supposed to prove this by showing two different sequences ${n_k}$ and ${k}$ converge. Other than that I am not sure…
Sam
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Minima for a Sum

Let $A=\{|a_i|:a_i\in\mathbb{Z}\land1\leq i\leq n\}$ and $n\geq 1$ Let $b_i=\frac{\max A}{|a_i|}.$ How can one prove that the minimum possible value for$\sum\limits_{i=1}^n b_i$ is $n$?
Maazul
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prove this equation has at least two real solutions

I want to prove that $2^x=2-x^2$ has at least two real solutions. I am trying to use Bolzano theorem to prove this, that is if $f(x)=2^x-2+x^2$=$0$ then $f(x)$ is continuous on R will be negative somewhere and positive somewhere and so satisfy…
LoveMath
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How to prove completeness of Bochner spaces?

How to prove that Bochner space $L^2(0,T; L^p(\Omega))$ is complete with norm $$\|f\|_{L^2(0,T; L^p(\Omega))} = \left(\int_0^T \|f(t)\|^2_{L^p} dt\right)^{\frac{1}{2}}$$ where $1
Mario
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Cauchy's formula on function at the pole not inside

How can one define the integral when the pole is on the integration contour? $$\int_{|w|=1}\dfrac{1}{i-w}\, dw$$
Abdelhamid Rehouma
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$x_1>x_0$ for $x_{n+1} = e^{\frac13(x_n-2)}$

I have this fixed point iteration for finding a solution of the given equation: $x_{n+1} = e^{\frac13(x_n-2)}$. I have to show that if $x_0=\beta+\epsilon$, where $\epsilon$ is a positive real number, then $x_1>x_0$. And also to deduce that this…
Bran
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A Question About Equicontinuous Family

Before we proceed with the question, let us introduce the following notations: Notations. $X$ and $Y$ are TVS over the field $\mathbb{R}$. $L(X,Y)$ is the space of all linear maps from $X$ into $Y$. $CL(X,Y)$ is the space of all continuous linear…
Juniven Acapulco
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Is it true that the function f(x) goes to 0 as n goes to infinity

Suppose that a function $f(x)$ defined on $[0,1]$ satisfies $f(1/n)\to 0$ as $n\to\infty$. Is it true that $f(x)\to 0$ as $x\to 0^+$ provided (a) $f$ is continuous on $[0,1]$ ? (b) $f$ is differentiable $(0,1)$ ? I know it will be true for example…
LoveMath
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