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Nov
21
comment Reconstructing a function from its critical points and inflection points
@whatever Well saddle points are just inflection points with the added property that $f'(x)=0$. I guess there are multiple names that are being used for both types hence the confusion. :)
Nov
21
comment Reconstructing a function from its critical points and inflection points
@whatever Every saddle point is an inflection point but not the other way round if I am not mistaken. The slope at a saddle is always zero while it does not have to be zero for inflection points.
Nov
21
revised Reconstructing a function from its critical points and inflection points
added 151 characters in body
Nov
21
comment Reconstructing a function from its critical points and inflection points
Because it is just a sketch to show how derivatives behave in the neighbourhood of critical points I left out specific values of $x$ and $f(x)$ hence you can pick whatever values that make this easier.
Nov
21
asked Reconstructing a function from its critical points and inflection points
Nov
19
awarded  Explainer
Nov
18
comment proof of limit explanation
@Silas2033 For the proof we use the following definition: Let $(x_n)_n$ be a sequence then $a\in\mathbb{R}$ is the limit of $(x_n)_n$ if there is a $N\in\mathbb{N}$ for each $\varepsilon > 0$ s.t. $$|x_n-a|<\varepsilon\qquad \text{for each }n\in\mathbb{N}\text{ with }n\geq N.$$ In my example there is such an $N$ for $\varepsilon=0.5$ with $N=3$ because the inequality holds for each $n\geq N$.
Nov
17
answered proof of limit explanation
Nov
17
accepted Show that $\exp(x)-1=\mathcal{O}(x)$ for $x\to 0$
Nov
17
asked Show that $\exp(x)-1=\mathcal{O}(x)$ for $x\to 0$
Nov
17
comment Prove that $\frac{b-a}{\cos^2 (a)}< \tan b - \tan a < \frac{b-a}{\cos^2 b}$
Did someone say Bill $\cos b$?
Nov
12
accepted Show that $\sqrt{x}$ is continuous using sequences
Nov
10
asked Show that $\sqrt{x}$ is continuous using sequences
Nov
7
comment Simplify $-2\sin(x)\cos(x)-2\cos(x)$
Factor out $-2\cos(x)$ and you get the desired result.
Nov
5
comment Is this true (Natural Logarithm)?
Keep in mind to not only include a negative, but a positive $\beta$ as well, i.e. $\beta=\pm\left(\ln(D)/\sqrt{\pi^2+\ln^2(D)}\right)$. Otherwise I see no error in your equivalence.
Nov
5
comment Showing an inequality: $\sqrt{xy} \leq \frac{2xy}{x+y}$
@elfeck Assume you have $x\leq y$ then you multiply it by $1/x$ to obtain $1\leq y/x$ and then with $1/y$ which yields $1/y\leq 1/x$, hence $x\leq y\Leftrightarrow 1/x\geq 1/y$. Just keep the right direction of the inequality in mind.
Nov
3
accepted Prove that $x_{n+1}=\frac{x_n}{2}+\frac{1}{x_n}\geq\sqrt{2}$
Nov
3
accepted Is there a whole number $x\in\mathbb{Z}$ with $x\neq 0$ s.t. $\exp(x)$ is natural?
Nov
3
revised Is there a whole number $x\in\mathbb{Z}$ with $x\neq 0$ s.t. $\exp(x)$ is natural?
Adjusted the title to the match the edited content.
Nov
3
comment Is there a whole number $x\in\mathbb{Z}$ with $x\neq 0$ s.t. $\exp(x)$ is natural?
@avid19 Please refer to my edit - it was a mistake to include 0.