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### Questions (64)

 11 Why does the definition of limits of a function have strict inequality? 8 Finding the limit of $\sqrt[n]{{kn \choose n}}$ 7 Limit of $\frac{f\left(x+g\left(x\right)\right)-f\left(g\left(x\right)\right)}{x}$ as $x\to 0$ 7 In field ($F, +, \cdot$) , how can I prove $x^2 =1\implies x=1,-1$ 6 All the ternary n-words with an even sum of digits and a zero.

### Reputation (914)

 +10 for $f\in C^2(\mathbb{R})$, finding the derivative of $\frac{d}{dt}\int_0^\infty f(x+t)\cdot xdx$ +10 Finding required sample size to get a good approximation of binomial distribution with unknown parameter $p$ using Central Limit theorem. +5 Proving the limit of the power of two functions is the power of the limits? +5 Expected value and sum of independent variables.

 3 If $\lim\limits _{x\to\infty}\left(\log f\right)'\left(x\right)$ is negative, then $\int_{0}^{\infty}f\left(x\right)dx$ converges? 2 For any closed set $A$ of $\mathbb R$ , does there exists a function $f:\mathbb R \to \mathbb R$ such that, $f$ is discontinuous exactly on $A$? 2 Evaluate $\lim \limits_{n\to \infty }\sin^2 (\pi \sqrt{(n!)^2-(n!)})$ 1 Analysis: Basic Sequence Proof 0 Finding the maximum of $f(x,y,z)=x^ay^bz^c$ where $x,y,z\in [0,\infty)$ and $x^k+y^k+z^k=1$

### Tags (57)

 6 real-analysis × 27 1 convergence 3 improper-integrals × 3 0 calculus × 9 2 limits × 5 0 derivatives × 6 2 algebra-precalculus 0 linear-algebra × 6 2 continuity 0 sequences-and-series × 6

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