hmedan.mnsh

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63 Questions

 42 Is there a function with the property$f(n)=f^{(n)}(a)$ 22 Find closed form for $1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, \ldots$ 18 Finding the fraction $\frac{a^5+b^5+c^5+d^5}{a^6+b^6+c^6+d^6}$ when knowing the sums $a+b+c+d$ to $a^4+b^4+c^4+d^4$ 12 integral of $\int \limits_{0}^{\infty}\frac {\sin (x^n)} {x^n}dx$ 11 closed form of $\int_{0}^{2\pi}\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^n}$

2,231 Reputation

 +33 Prove that $\int_0^{\infty} \frac{t^n} {1+e^t}dt=(1-2^{-n})n!\zeta (n+1)$ +5 what is the proper contour for $\int_{-\infty}^{\infty}\frac{e^z}{1+e^{nz}}dz$ +5 closed form of $\int_{0}^{2\pi}\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^n}$ +5 Find the limit without use of L'Hôpital or Taylor series: $\lim \limits_{x\rightarrow 0} \left(\frac{1}{x^2}-\frac{1}{\sin^2 x}\right)$

 12 Find the value of $3^9\cdot 3^3\cdot 3\cdot 3^{1/3}\cdot\cdots$ 7 Find the limit without use of L'Hôpital or Taylor series: $\lim \limits_{x\rightarrow 0} \left(\frac{1}{x^2}-\frac{1}{\sin^2 x}\right)$ 5 Is there any formula for summation? 4 Compute $\int_{-\infty}^{\infty} \frac{x^2}{(1+x^2)^2} dx$ 4 Starting with $\frac{-1}{1}=\frac{1}{-1}$ and taking square root: proves $1=-1$

59 Tags

 35 calculus × 34 12 recreational-mathematics 17 integration × 24 9 real-analysis × 4 16 limits × 11 7 algebra-precalculus × 5 12 infinite-product × 2 7 trigonometry × 4 12 problem-solving 6 summation × 8

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