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 12 Is $2^{218!} +1$ prime? 11 How can I prove that $xy\leq x^2+y^2$? 9 Prove $(1-\cos x)/\sin x = \tan x/2$ 7 How do you find the limit of $\lim_{x \to 0} \frac{1-e^{6x}}{1-e^{3x}}$ 6 Mental estimate for tangent of an angle (from $0$ to $90$ degrees)

### Reputation (699)

 +10 Prove $(1-\cos x)/\sin x = \tan x/2$ +10 Is $2^{218!} +1$ prime? +5 A curious fact on partitions of 7 integer and related question. -2 Differential equation: $y'-\tan x \cdot y=e^{2x}$

### Questions (4)

 3 A curious fact on partitions of 7 integer and related question. 1 Nested square root of continued fraction references 1 The unbeatable $\int e^{1/\cos(x)} dx$ integral 0 Limits and digit sums

### Tags (28)

 17 trigonometry × 3 7 limits × 2 13 inequality × 2 6 mental-arithmetic 12 prime-numbers × 2 6 estimation 12 elementary-number-theory 2 functions × 2 11 real-analysis × 2 2 sequences-and-series

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