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Jan
26
awarded  calculus
Jan
25
comment Limit $\lim_{x \to 0} \dfrac{\sin(1-\cos x)}{ x} $
I'm fully aware, but the OP may not be.. @Arthur
Jan
25
answered Limit $\lim_{x \to 0} \dfrac{\sin(1-\cos x)}{ x} $
Jan
25
revised How to evaluate $\int _0^{2\pi }\int _0^{\frac{\pi }{4}}\int _0^{\frac{1}{\cos\phi }}\:\:\:\rho ^2\sin\left(\phi \right)d\rho \:d\phi \:d\theta $?
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Jan
25
answered How to evaluate $\int _0^{2\pi }\int _0^{\frac{\pi }{4}}\int _0^{\frac{1}{\cos\phi }}\:\:\:\rho ^2\sin\left(\phi \right)d\rho \:d\phi \:d\theta $?
Jan
24
comment Euler-Maclaurin formula for half integer values in summation
The formula needs no adjusting, just apply it to $g(n)=f(n+1/2)$.
Jan
23
revised Find if $\sqrt[4]{x^4+y^4}, \sqrt{x^4+y^4}$ are differentiable in $(0,0)$
This is not functional analysis.
Jan
23
comment Continuity of Popcorn Function (Thomae's Function)
For $f$ to be continuous at $a$ you need to show that $\lim_{n\to\infty} f(x_n)=f(a)$ for all sequences $(x_n)_n$ with $x_n\to a$, not just your favorite one.
Jan
23
answered $(\mathbb{R}^n,\|\cdot\|_{p})$ is isometrically isomorphic to $(\mathbb{R}^n,\|\cdot\|_{q})$ iff $p=q,$
Jan
23
answered How to show that $\frac{\ln x}{x}$ is monotone for $x\ge e$?
Jan
22
comment Evaluate $\int_{\pi}^{3 \pi/2}\frac{1}{1-\rho \sin{2 \theta }} d\theta$
There is a general trick for integrating rational functions of trigonometric functions by substituting $t=\tan(x/2)$.
Dec
10
answered $L^2$ mapping is necessarily onto or not?
Dec
10
revised Graph of $y=x^x$ for $x<0$
deleted 4 characters in body
Nov
29
comment Showing that a subset of $\ell^1$ is totally bounded
What? No, $A$ is not closed. There is a $<$ in the definition of $A$.
Nov
28
comment Showing that a subset of $\ell^1$ is totally bounded
@Sarita Sharma: do you understand?
Nov
28
comment For every $f \in L^1(\mathbb{R})$, do we have $\sup_{n \in \mathbb{N}}|T_nf(x)| < \infty$ for a.e. $x$?
Try plugging in an unbounded integrable function, like $f=x^{-1/2} \chi_{|x|\le 1}$.
Nov
26
revised Showing that a subset of $\ell^1$ is totally bounded
deleted 4 characters in body
Nov
26
revised Showing that a subset of $\ell^1$ is totally bounded
fixed grammar, formatting, spelling
Nov
26
answered Showing that a subset of $\ell^1$ is totally bounded
Nov
23
revised A natural proof of the Cauchy-Schwarz inequality
added link