Question

Four rational numbers between 2 and 3

Answer 1

$\mathrm{a}_{\mathrm{n}}=\int_{0}^{\frac{\pi}{2}} \frac{1-\cos 2 \mathrm{nx}}{1-\cos \mathrm{x}} \mathrm{dx},a </p><p>n</p><p> =∫ </p><p>0</p><p>2</p><p>π</p><p> </p><p> </p><p>1−cosx</p><p>1−cos2nx</p><p> dx, then \mathrm{f}(\mathrm{x})=\left|\begin{array}{lll}\mathrm{a}_{1} & \mathrm{a}_{2} & \mathrm{a}_{3} \\ \mathrm{a}_{4} & \mathrm{a}_{5} & \mathrm{a}_{6} \\ \mathrm{a}_{7} & \mathrm{a}_{8} & \mathrm{a}_{9}\end{array}\right| \forall \mathrm{x} \in \mathrm{R} ;f(x)=$

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a

1

a

4

a

7

a

2

a

5

a

8

a

3

a

6

a

9

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∀x∈R; then \mathrm{f}(1)=f(1)=

Answer 2

Answer:

11/5, 12/5, 13/5, 14/5

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