### Answers (608)

 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.

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