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 Mar 9 comment Prove that $\displaystyle \lim_{x \to a} f(x) = \infty$ iff $\displaystyle \lim_{x \to a} \frac{1}{f(x)} = 0$ @Puzzled417 it is talking about the same $f$ in the second part... Mar 7 comment Prove that $\displaystyle \lim_{x \to a} f(x) = \infty$ iff $\displaystyle \lim_{x \to a} \frac{1}{f(x)} = 0$ @Puzzled417 But $M = 1/\epsilon > 0$ and so $f(x) > 0$ too Mar 7 comment How to derive cosine difference formula? Are you looking to expand $$\cos(x-y) = \cos x \cos y + \sin x \sin y$$ or simplify $$\cos x - \cos y?$$ Mar 7 comment Exponential conjugate equals to reciprocal? @newbie125 i don't think it simplifies this easily as your example, unfortunately Mar 6 comment Nested trig asymptotics so it's really a $\sum_{k=1}^n \sin^k (\pi/2)$, not $\int_{x=1}^n \sin^x(\pi/2)$? Mar 6 comment Linear program solved with Simplex out of given bound i think your solution is not feasible, so the max value of $146$ is ok -- it can be more if it does not satisfy the constraints. Mar 6 comment PrimeQ[ Table[sum_(n=1)^(N)n!, {N,1,30}]] what do you want to find? Mar 6 comment Can someone help me out with this question about logs? please How do you know that $x,y \in \mathbb{Z}$? Mar 6 comment Exponential conjugate equals to reciprocal? @newbie125 i dont understand - what do you want to find? $$\sum_{k=1}^n \frac{1}{\sin k}?$$ Mar 6 comment Integration in many variables. that's a restriction on $f$, you likely want to update your question with that assumption in place. Please look at Fubini's theorem (en.wikipedia.org/wiki/Fubini%27s_theorem) in the section for integrable functions Mar 6 comment Integration in many variables. i don't think this is generally true, are there any restrictions on $f$? Mar 6 comment On differentiable functions on real line satisfying $f'(x)\ge f(x)^2 , \forall x>0$ @Arthur indeed, at $t = -C$ we have issues. But he only needs for $t >0$ so any $C < 0$ will do, and we have an entire class of functions that satisfy that condition. Mar 4 comment Prove that $\left|\frac{e^{-ht}-1}{h}\right|\le t$ for $h>0$ +1, very clever use of MVT Mar 1 comment How do I represent this in terms of m and x i think you just proved that $E$ is independent of $x$... Mar 1 comment Simply this formula what is $\sum [\cdot]$ can you please rewrite your formulae to make them readable? Feb 23 comment Partition of number's squares The first $n$ I can see this is possible for is $n=8$, and the greedy algorithm from the largest number produces the partitioning. Not sure this will or will not work for $n=1000$ Feb 23 comment Partition of number's squares Why do you think this is necessarily possible? Feb 23 comment The function $f (x) = f \left (\frac x2 \right ) + f \left (\frac x2 + \frac 12\right)$ the only thing i can see is that $$f(x+1)-f(x) = f(x/2+1)-f(x/2)$$ and $f(1/2)=0$ Feb 22 comment $\sigma$-algebra generated by a subset @Clarinetist, no, it's the smallest also because it is the minimum extension of the current set to a sigma-algebra. So suffices to find one, and show that none of its subsets are sigma algebras. Feb 22 comment How to find second order derivative when i posted an answer, i made a mistake in calculations, so i thought i well knew what the answer was. as for this comment, it is not an answer, just a suggestion along which lines i would think...