New posts in real-analysis

Prove that there exist $a \in [-1,1]$, such that $f'''(a)=3f(1)-3f(-1)-6f'(0)$

calculus real-analysis derivatives

Application of the chain rule to $3$-layers neural network

real-analysis statistics multivariable-calculus machine-learning neural-networks

Why "a function continuous at only one point" is not an oxymoron?

real-analysis continuity

Construction of a continuous function which is not bounded on given interval.

real-analysis continuity

Derivative and constant function

calculus real-analysis

Prove that $\lim\limits_{n\rightarrow \infty}\int_1^3\frac{nx^{99}+5}{x^3+nx^{66}} d x$ exists and evaluate it.

real-analysis limits

Asymptotic Expansion of an Oscillating Integral

real-analysis integration asymptotics

$L^{p}$ functions from Rudin Exercises 3.5

real-analysis probability-theory lebesgue-integral lp-spaces

What is the relation between Locally Compact Hausdorff Spaces and Complete Separable Metric Spaces?

real-analysis functional-analysis analysis

Is this sufficient to prove that $xe^x$ is invertible and its inverse is differentiable from $(0,\infty)$?

$(x_n)$ is a sequence of positive numbers. If $\lim n \log\frac{x_n}{x_{n+1}}\gt 1$ then is it true that the series $\sum x_n$ converges? [duplicate]

real-analysis calculus

Prob. 3, Sec. 3.4, in Bartle & Sherbert's INTRO TO REAL ANALYSIS, 4th ed: Does this sequence converge?

real-analysis sequences-and-series analysis limits convergence-divergence

Range of bounded operator is of first category

real-analysis functional-analysis banach-spaces

Prove that $\exists a, b\in(0,1)$ such that $\int_0^{a} xf(x)dx=0\text{ and }\int_0^bxf(x)dx=\frac{b^2f(b)}{2}.$

real-analysis integration

If $f$ has a vanishing (first or higher) derivative at every point, $f$ is a polynomial

calculus real-analysis analysis polynomials

How can I prove that a function is uniquely differentiable?

is there example that inequality $\sup\{\inf\{f(x,y) : x \in X\}: y \in Y\} \le \inf\{\sup\{f(x,y) : y \in Y\}: x \in X\}$ be strict?

real-analysis analysis supremum-and-infimum

Show $(a_1+···+a_n)^2 ≤ n(a^2_1+···+a^2_n).$ [duplicate]

real-analysis solution-verification

Exercise 6.9 in Rudin's RCA (Real and Complex Analysis)

real-analysis analysis

On continuity of roots of a polynomial depending on a real parameter

real-analysis complex-analysis algebraic-topology continuity