共50条信息
已知\(1\leqslant a\leqslant 3\),\(-4 < b < 2\),则\(a+|b|\)的取值范围是________.
\(\sqrt{2}+\sqrt{10}\)________\(2\sqrt{6}.(\)填\( > \)或\( < \)或\(=)\)
若\(a{,}b{,}c{∈}R\),则下列说法正确的是\(({ }\ { })\)
设\(a=\int _{1}^{2} \dfrac{1}{x}dx,b=\int _{1}^{3} \dfrac{1}{x}dx,c=\int _{1}^{5} \dfrac{1}{x}dx \),则下列关系式成立的是\((\) \()\)
已知非零实数\(a,b\)满足\(a > b\),则下列不等式成立的是 \((\) \()\)
已知\(α∈( \dfrac{π}{4}, \dfrac{π}{2})\),\(a=(\cos α)^{\cos \;α}\),\(b=(\sin α)^{\cos \;α}\),\(c=(\cos α)^{\sin \;α}\),则\((\) \()\)
下面四个命题:
\(①\)若\(a > b\), 则\(\dfrac{a}{b} > \dfrac{b+1}{a-1}\);
\(②\)若\(a > b > c > 0\),则\(\dfrac{a-c}{c} > \dfrac{b-c}{b}\);
\(③\)若\(a < b < 0\),则\(\dfrac{1}{a-b} > \dfrac{1}{a}\) ;
\(④\)若\(a > |b|\),则\({{a}^{2}} > {{b}^{2}}\)
上式中成立的是___________
\((2)\)若\(x∈\left(0,1\right) \)时不等式\(f\left(x\right) > x \)成立,求\(a\)的取值范围.
命题“若\(a > b\),则\(ac^{2} > bc^{2}(a,b,c∈R)\)”与它的逆命题、否命题,逆否命题中,真命题的个数为 \((\) \()\)
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