30 Finding $\prod_{n=1}^{999}\sin\left(\frac{n \pi}{1999}\right)$ 27 The last digit of $2^{2006}$ 19 Using the definition of derivative to evaluate $(\sin^2(x))'$ 19 Find the value of $\space\large i^{i^i}$? 18 L'hospital rule for two variable.

### Reputation (13,733)

 +10 $\lim_{x \to 0} \frac{e^{\sin^2 x} - \cos x}{x^3}$ +10 Can we call domain as inverse image of a function? +10 $\int_{-\infty}^\infty e^{ikx}dx$ equals what? +10 $f(x)=x^n+5x^{n-1}+3$ can't be expressed as the product of two polynomials

### Questions (21)

 28 Additivity + Measurability $\implies$ Continuity 24 Prove: Every compact metric space is separable 23 Expressing $2002^{2002}$ as a sum of cubes 19 Find all primes $p$ such that $\dfrac{(2^{p-1}-1)}{p}$ is a perfect square 8 $f(x)=x^n+5x^{n-1}+3$ can't be expressed as the product of two polynomials

### Tags (156)

 183 calculus × 76 81 elementary-number-theory × 27 125 algebra-precalculus × 46 51 real-analysis × 23 123 trigonometry × 34 48 integration × 23 116 limits × 40 45 modular-arithmetic × 9 89 sequences-and-series × 31 43 derivatives × 14

### Bookmarks (21)

 716 Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem) 267 Funny identities [closed] 77 Direct proof that $\pi$ is not constructible 29 IMO 1987 - function such that $f(f(n))=n+1987$ [closed] 28 Additivity + Measurability $\implies$ Continuity

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