共50条信息
已知\(1\leqslant a\leqslant 3\),\(-4 < b < 2\),则\(a+|b|\)的取值范围是________.
\((2)\)若\(x∈\left(0,1\right) \)时不等式\(f\left(x\right) > x \)成立,求\(a\)的取值范围.
设\(a={{\log }_{0.2}}0.3\),\(b={{\log }_{2}}0.3\),则\((\) \()\)
\((2)\)若\(f(-\dfrac{3}{2}) < 3\),求实数\(a\)的取值范围.
给出下列命题:\(①\)若\(b < a < 0\),则\(|a| > |b|\);\(②\)若\(b < a < 0\),则\(a+b < ab\);\(③\)若\(b < a < 0\),则\(\dfrac{b}{a}+\dfrac{a}{b} > 2\);\(④\)若\(b < a < 0\),则\(\dfrac{{{a}^{2}}}{b} < 2a-b\);\(⑤\)若\(b < a < 0\),则\(\dfrac{2a+b}{a+2b} > \dfrac{a}{b}\);\(⑥\)若\(a+b=1\),则\({{a}^{2}}+{{b}^{2}}\geqslant \dfrac{1}{2}.\)其中正确的命题有\((\) \()\)
定义在\(R\)上的奇函数\(f(x)\),当\(x\in (-\infty ,0)\)时,\(f(x)+x{f}{{{"}}}(x) < 0\)恒成立,若\(a=3f(3)\),\(b=({{\log }_{\pi }}3)\cdot f({{\log }_{\pi }}3)\),\(c=-2f(-2)\),则
如果\(a > b > 1\),\(c < 0\),在不等式\(①\dfrac{c}{a} > \dfrac{c}{b}\);\(②\ln \left( a+c \right) > \ln \left( b+c \right)\);\(③{{\left( a-c \right)}^{c}} < {{\left( b-c \right)}^{c}}\);\(④b{{e}^{a}} > a{{e}^{b}}\)中,所有正确命题的序号是\((\) \()\)
若对于任意的\(0 < x_{1} < x_{2} < a\),都有\(\dfrac{{{x}_{2}}\ln {{x}_{1}}-{{x}_{1}}\ln {{x}_{2}}}{{{x}_{1}}-{{x}_{2}}} > 1\),则\(a\)的最大值为\((\) \()\)
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