sin30 <sin69

cos81<cos40

\(sin30^0< sin69^0\)

\(cos81^0< cos40^0\)

Ta có:

\(3^{39}< 3^{42}\)

Mà: \(3^{42}=\left(3^2\right)^{21}=9^{21}\)

Lại có: \(9< 11\Rightarrow9^{21}< 11^{21}\)

\(\Rightarrow3^{39}< 11^{21}\)

Ta có: 

\(5^{217}>5^{216}\)

Mà: \(5^{216}=5^{3\cdot72}=\left(5^3\right)^{72}=125^{72}\)

Lại có: \(125>119\Rightarrow125^{72}>119^{72}\)

\(\Rightarrow5^{216}>119^{72}\)

\(\Rightarrow5^{217}>119^{72}\)

\(201^{60}=\left(201^4\right)^{15}=1944810000^{15}\)

\(398^{45}=\left(398^3\right)^{15}=63044792^{15}\)

Do \(1944810000>63044792\)

\(\Rightarrow1944810000^{15}>63044792^{15}\)

\(\Rightarrow201^{60}>398^{45}\)

Ta có:

\(201^{60}>200^{60};398^{45}< 400^{45}\)

\(200^{60}=\left(2.100\right)^{60}=2^{60}.100^{60}=2^{60}.\left(10^2\right)^{60}\)

\(=2^{60}.10^{120}=2^{60}.10^{30}.10^{90}\)

\(400^{45}=\left(2.100\right)^{45}=2^{45}.100^{45}=2^{45}.\left(10^2\right)^{45}\)

\(=2^{45}.10^{90}\)

Mà \(2^{60}.10^{30}.10^{90}>2^{45}.10^{90}\)

\(\Rightarrow200^{60}>400^{45}\)

\(\Rightarrow201^{60}>200^{60}>400^{45}>398^{45}\)

\(\Rightarrow201^{60}>398^{45}\)

1) `-3\sqrt13=-3\sqrt13`

`-9=-3\sqrt9`

`\sqrt13>\sqrt9`

`=> -3\sqrt13 < -3\sqrt9`

`=> -3\sqrt13 < 9`.

2) `\sqrt15 < \sqrt16`

`<=> \sqrt15-1 < \sqrt16-1`

`<=> \sqrt15-1 < 3 < \sqrt10`

`=> \sqrt15-1 <\sqrt10`

3) `5=4+1=\sqrt16+1`

`\sqrt8+1=\sqrt8+1`

`=> 5>\sqrt8+1`

1) \(-3\sqrt{13}=-\sqrt{117}< -\sqrt{81}=-9\)

3) Ta có: \(5^2=25=9+16\)

\(\left(2\sqrt{2}+1\right)^2=9+4\sqrt{2}\)

mà \(16>4\sqrt{2}\)

nên \(5>2\sqrt{2}+1\)

a: so sánh với 1

64/85 < 73/81

b: so sánh với 1 

n + 1/n+2 > n/ n+3

c: so sánh với 1

64/65 > 60/61

d: so sánh với 1

99/97 < 88/86

27/31<2727/3131

11/31<111/311

A=1/1*3+1/3*5+...+1/9*11+1/11*13

=1/2(1-1/3+1/3-1/5+...+1/11-1/13)

=1/2*12/13=6/13<B

a) \(\frac{29}{60}< \frac{1}{2}< \frac{15}{28}\)

b)\(\frac{13}{30}< \frac{1}{2}< \frac{23}{42}\)

c)\(\frac{13}{36}>\frac{1}{3}>\frac{14}{45}\)

d)\(\frac{1919}{9595}=\frac{1}{5}< \frac{11}{50}=\frac{1111}{5050}\)

chúc các bạn học tôt nhớ k đúng cho mình nha !!!!!!!!!!!!!!!!!!!!!!!!!!!!!