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 11 How can I prove that $xy\leq x^2+y^2$? 11 Is $2^{218!} +1$ prime? 8 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 (679)

 +5 A curious fact on partitions of 7 integer and related question. -2 Differential equation: $y'-\tan x \cdot y=e^{2x}$ +10 How can I prove that $xy\leq x^2+y^2$? +10 $2^{1/4} \times 4^{1/8} \times 8^{1/16} \times 16^{1/32} \times \ldots\to2$

### 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 (29)

 16 trigonometry × 3 11 elementary-number-theory 13 inequality × 2 7 limits × 2 11 prime-numbers × 2 6 mental-arithmetic 11 real-analysis × 2 6 estimation 11 proof-strategy 2 functions × 2

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