miracle173
Reputation
3,083
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
11 28
Newest
Impact
~65k people reached

• 7 helpful flags
• 721 votes cast

# 1,033 Actions

 Nov25 comment Why can ALL quadratic equations be solved by the quadratic formula? $x-\alpha = x-\beta = 0$ would imply $\alpha=\beta=0$. Your proof needs the theorem from vieta. I can't see how you get to the result by adding equations 2 and 3 as you stated in the text. Sorry, but the whole proof is rather complicated and rather boring. Nov24 reviewed Reject An analytic characterization of eigenvalues of a Hermitan matrix. Nov24 comment How to find the sum of this : $\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+ \sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+…$ @user158108: $$n^2 \cdot (n+1)^2 + n^2 + (n+1)^2=n^4+2 n^3+3 n^2+2 n+1$$ But polynomial equations of type $$x^4+ax^3+bx^2+ax+1=0$$ can be transformed to $$(x^4+1)+ax(x^2+1)+bx=0$$ and further to $$x^2((x+\frac{1}{x})^2-2)+a(x+\frac{1}{x})+c)=0$$ Now the substitution $$y=x+\frac{1}{x}$$ can be used. Nov24 reviewed Approve What is this called: $\frac{\partial^2f}{\partial x^2} + \frac{\partial^2f}{\partial y^2} =$ … Laplacian? Nov24 comment An interesting table of Prime Generating polynomials similar to $n^2+n+41$? To me it seems that these are at least 5 questions. Nov24 reviewed Approve Low rank approximation using CVX toolbox in Matlab Nov24 comment Prove that $F(1) + F(3) + F(5) + … + F(2n-1) = F(2n)$ and you start with which $n$? For $n=1$ you get $0=f(1)=f(2)=?$ Nov24 answered Prove that $F(1) + F(3) + F(5) + … + F(2n-1) = F(2n)$ Nov24 comment Prove that $F(1) + F(3) + F(5) + … + F(2n-1) = F(2n)$ Why do you use two different notations for the numbers? Either $f(n)$ of $F(n)$. Then numbers are $0,1,1,2,3,5,\ldots$. So if $f(5)=5$ then $f(1)=1, f(3)=2$. Nov24 reviewed Edit Solving this trigonometric task Nov24 revised Solving this trigonometric task Replaced photo of equation with actual LaTEX. Nov23 revised $x,y,z$ are positive real numbers and $x+y+z=1$ $\implies$ $\bigg(1+\dfrac 1x\bigg)\bigg(1+\dfrac 1y \bigg)\bigg(1+\dfrac 1z \bigg)\ge 64$? typo Nov23 revised Prove $\text{rad}(I)/I$ is isomorphic to $\mathfrak{N}(R/I)$ latex Nov23 reviewed Approve Finding a limit for n tends to infinity Nov23 reviewed Approve Determine if $\displaystyle \int_3^{\infty}\frac{x+1}{\sqrt{x^4-x}}\,dx$ converges Nov21 comment $P(x+2)=2x^3-4x^2+2x+3$. Find the remainder of $\dfrac{P(x)}{(x-3)}$ What does $P(u)=2(x-2)^3-4(x-2)^2+2(x-2)+3$ mean? Do you want the remainder of $P(x)/x-3=\frac{P(x)}{x}-3$ or of $P(x)/(x-3)=\frac{P(x)}{x-3}$ Nov19 comment What is indefinite integral actually - $\int f(x)dx$ or $\int_a^x f(t)dt$? How is a function $F(x)=\int_0^xf(t)dt$ connected with the antiderivates? It is an antiderivate of $f$ if $f$ is continous, so $F'(x)=(\int_0^xf(t)dt)'=f(x)$. To see this one has to proof that $\lim_{h \to 0} \frac{F(x+h)-F(x)}{h}=\lim_{h \to 0} \frac{\int_0^{x+h}f(t)dt-\int_0^xf(t)dt}{h}=\lim_{h \to 0} \frac{\int_x^{x+h}f(t)dt}{h}$ is equal to $f(x)$ Nov19 comment What is indefinite integral actually - $\int f(x)dx$ or $\int_a^x f(t)dt$? For example select $a=0$ and $f(t)=t^2$ and therefore $F(x)=\int_0^x t^2 dt$. So for $x=3$ the function value $F(3)$ is the definite integral $\int_0^3 t^2 dt$, which is $9$, for $x=4$ the function value $F(4)$ is the definite integral $\int_0^4 t^2 dt$, which is $64/3$ Nov19 reviewed Approve What is indefinite integral actually - $\int f(x)dx$ or $\int_a^x f(t)dt$? Nov19 revised Arrange in increasing order of asymptotic complexity latex, removed png