Hagen von Eitzen
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 Apr 25 comment Why doesn't L'Hospital's rule work for this limit? The rule (for this particular indeterminate form) says: If $f(x)\to \infty$ and $g(x)\to \infty$ and $\lim\frac{f'(x)}{g'(x)}$ exists, then $\lim\frac{f'x)}{g(x)}$ exists and equals $\lim\frac{f'(x)}{g'(x)}$. Apr 25 comment The sum of two numbers is 5/9… I read the last instruction as asking for $(0.4 x)\cdot (0.4y)$ Apr 25 answered Does there exist a complex function which is differentiable at one point and nowhere else continuous? Apr 25 comment Has the polynomial distinct roots? How can I prove it? @drxy I found my counterexample by just playing around with $\gcd(f,f')$, motivated by mathguy's solution for real roots. I'm sure that playing around will also allow finding counterexamples (regarding complex roots) for higher $p$ values one by one - but the handling becomes impractical. Apr 25 comment Prisoners and hats variation Do they guess only once? OR is the game repeted (with the same hats) if nobody dared to guess? Apr 25 comment $\sup\limits_{t>0}[\frac{g(t)}{\sup\limits_{t \beta$ or not? deleted 1 character in body Apr 25 comment The $\cos(\alpha-\beta)$ formula always need $\alpha > \beta$ or not? @user3270418 Where do I show the sum formula? I read $\cos(\alpha-\beta)$ in my post. Apr 25 answered Significance of derivative in finding square free decomposition Apr 25 answered Deterministic finite automaton parity bit question Apr 25 comment The $\cos(\alpha-\beta)$ formula always need $\alpha > \beta$ or not? Are you sure your argument leads to a "No"? - Oh, you seemingly answered the title question, which is the opposite of the body question ... Apr 25 comment The $\cos(\alpha-\beta)$ formula always need $\alpha > \beta$ or not? @user3270418 No, I mean what I wrote. For $\alpha=\beta=60^\circ$, we have $\cos(60^\circ)^2+\sin(60^\circ)^2=(1/2)^2+(\sqrt 3/2)^2=1/4+3/4=1$ Apr 25 answered The $\cos(\alpha-\beta)$ formula always need $\alpha > \beta$ or not? Apr 24 answered Show that there is a step function $g$ over $[a,b]$ Apr 24 comment Is there a way to write an infinite set that contains only irrational numbers without integer multiples? In the same spirit as the last, $\{\,q\sqrt 2\mid q\in \Bbb Q\cap [1,2)\,\}$ Apr 24 comment The maximum of the absolute value of a real-valued function You could simply use that $\sup\bigcup_{i\in I}A_i =\sup_{i\in I}sup A_i$ Apr 24 answered Probability of seeing a headlight getting switched on