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 Apr 5 comment Error approximation of Simpson's rule Isn't the denominator $180n^4$? Apr 5 comment Error approximation of Simpson's rule The error is less than or equal to the absolute value of the quantity you wrote--it's not exactly equal to it. $c$ is the point where $|f^{(4)}(c)|$ is maximum on $[a,b]$, so there can be more than one point where $|f^{(4)}(x)|$ achieves a maximum on $[a,b]$. Mar 25 answered Show that $SL(n, \mathbb{R})$ is a $(n^2 -1)$ smooth submanifold of $M(n,\mathbb{R})$ Mar 25 comment Show that $SL(n, \mathbb{R})$ is a $(n^2 -1)$ smooth submanifold of $M(n,\mathbb{R})$ Awesome. This is so much better than what I had in mind. Mar 25 answered $|x-2|$ as a factor of $|x^n-2^n|$ as a limit of function Mar 25 comment $|x-2|$ as a factor of $|x^n-2^n|$ as a limit of function It might be helpful to regroup and use triangle inequality: $|x^{n-1}-2^{n-1}+2(x^{n-2}-2^{n-2})+2^2(x^{n-3}-2^{n-3})+\dots+2^{n-2}(x-2)|$. Mar 4 comment Applying the Taylor's Theorem, show that if $x > 0$ then $|(1+x)^{1/3} - (1 + \frac x3 - {x^2\over 9})| \le {5x^3\over 81}$ @Did You are saying that the alternating series estimation applies only for $0\le x\le1$, right? Because that is where the series is both alternating and convergent? Mar 3 awarded Popular Question Feb 27 comment Proving that the analytic function $f$ is constant. @SMath $|f(z)|^2=f(z)\bar{f(z)}=c$. Take the derivative with respect to $z$ using the Leibniz rule. Feb 3 comment How to compute $\lim\limits_{x \rightarrow 0} \frac{1}{x^2}\int_0^{G(x)} \arctan(s+2s^2) ds$ Are you familiar with the Fundamental theorem of calculus? There are two versions of it. Jan 20 revised Definition of limit of sequences in text (Taylor's Foundation of Analysis) added 1 character in body Jan 20 revised Show that the error $\mid f(x)-P_2(x) \mid$ is bounded by $\frac{\sqrt2e}{3}$ on $[0,1]$ added 9 characters in body Oct 14 awarded Yearling Jul 4 comment Hardcore Abstract Algebra Book Request Yeah, it sounds like you want Lang. Jul 2 reviewed Leave Open How to solve Probability questions? Jul 2 reviewed Leave Open Online tool to check if number is rational or irrational? Jul 2 reviewed Leave Open Evaluate the following Integration-- Jul 2 reviewed Leave Open Optimal approximation of quadratic form Jul 1 reviewed Leave Open How do we use derivatives in our daily lives Jun 29 awarded Custodian