RE60K

 59 Are all limits solvable without L'Hôpital Rule or Series Expansion 24 The limit of the alternating series $x - x^2 + x^4 - x^8 + {x^{16}}-\dotsb$ as $x \to 1$ 20 Some clever trick is required for this Integral with irrational power of cosine as integrand. 16 Lottery odds calculated in your head, or pen and paper. 14 How to find $\lim_{x \to 0} ( \frac{1}{\sin(x)}- \frac{1}{\arcsin(x)})$

### Reputation (14,193)

 +30 Are all limits solvable without L'Hôpital Rule or Series Expansion +10 How to derive the equation of a parabola given a focus and a directrix not parallel to the x or y axis? +10 How to prove inequality $\frac{a}{a+bc}+\frac{b}{b+cd}+\frac{c}{c+da}+\frac{d}{d+ab}\ge 2$ +5 How to prove sum of powers property of roots of unity?

### Questions (158)

 21 Integrate $\int\sqrt\frac{\sin(x-a)}{\sin(x+a)}dx$ 18 Why maximum/minimum of linear programming occurs at a vertex? 10 Some clever trick is required for this Integral with irrational power of cosine as integrand. 10 Finding this summation: $\sum_{n=1}^{\infty}\frac{(2n+99)!(3n-2)!}{(2n)!(3n+99)!}$ 9 Change of variable in integration causes upper and lower unequal limits to be same and makes finite integral zero.

### Tags (202)

 273 calculus × 160 60 sequences-and-series × 37 191 integration × 125 59 definite-integrals × 27 186 limits × 67 49 combinatorics × 61 121 trigonometry × 67 44 geometry × 40 86 limits-without-lhopital × 8 44 indefinite-integrals × 21