2012ssohn

 27 Tricky Triangle Area Problem 14 Find the value of a+b+c 12 Proving that $\frac{e^x + e^{-x}}2 \le e^{x^2/2}$ 11 If $\frac{d}{dx}e{^x} = e{^x}$, then why does $\frac{d}{dx}e^{-14}$ = 0? 11 Proving a trig identity: $\frac{\sin(A + B)}{\sin(A - B)}=\frac{\tan A + \tan B}{\tan A - \tan B}$

### Reputation (3,747)

 +10 Evaluate $\int \frac{\sqrt{x^2-1}}{x} \mathrm{d}x$ +10 Need help understanding this integration by substitution: $\int \sec^{2}{x} \tan^{3}{x} \, \mathrm{d}x$ +10 Solutions to $x+y+z=31$ and $x+2y+3z=41$ +10 Probability of an airplane crash

### Questions (4)

 4 What is $\lim_{n \to \infty} \sum_{x=0}^{n-1} \frac{n-x}{n+x}$? 3 $f(1+x) = f(x)$ for all real $x$, $f$ is a polynomial and $f(5) = 11$. What is $f\large(\frac{15}{2}\large)$? 3 Different ways to evaluate $\displaystyle \underbrace{2^{2^{2^{\cdot^{\cdot^{\cdot^{2}}}}}}}_n$ 1 A system of simultaneous equations

### Tags (70)

 46 calculus × 22 27 area 33 geometry × 4 27 contest-math 29 algebra-precalculus × 13 26 trigonometry × 12 29 triangles × 2 23 exponential-function × 2 27 probability × 8 19 polynomials × 4

### Bookmarks (14)

 430 Proofs that every mathematician should know. [closed] 37 Is there a power of 2 that, written backward, is a power of 5? 31 Iterated exponent of $i$ 26 How prove this sum $\sum_{n=1}^{\infty}\binom{2n}{n}\frac{(-1)^{n-1}H_{n+1}}{4^n(n+1)}$ 15 What is $\int_{0}^{\pi}\frac{x}{x^2+\ln^2(2\sin x)}\:\mathrm{d}x$?