共50条信息
已知\(a,b,c,d,e,f,g\)是和为\(1\)的非负实数, \(M=max\{a+b+c, b+c+d,c+d+e,d+e+f,e+f+g\}\)则\(M\)的最小值为 \((\) \()\)
以下四个命题,其中正确的命题有( )
\(①\)若\(a\),\(b∈R\),则\(|a+b|-2|a|\leqslant |a-b|\);\(②\)若\(|a-b| < 1\),则\(|a| < |b|+1\);
\(③\)若\(|x| < 2\),\(|y| > 3\),则\(|\)\( \dfrac{x}{y}\)\(| < \)\( \dfrac{2}{3}\);\(④\)若\(AB\neq 0\),则\(\lg \)\( \dfrac{|A|+|B|}{2}\)\(\geqslant \)\( \dfrac{1}{2}\)\(( \lg |A|+\lg |B|)\).
已知\(f\left(x\right)=\left|x+1\right|-\left|ax-1\right| \).
\((1)\)当\(a=1\)时,求不等式\(f\left(x\right) > 1 \)的解集;
\((2)\)若\(x∈\left(0,1\right) \)时不等式\(f\left(x\right) > x \)成立,求\(a\)的取值范围.
下列命题
\(①\)“\(am^{2} < bm^{2}\)”是“\(a < b\)”的充分必要条件.
\(②\)“矩形的两条对角线相等”的否命题为假.
\(③\) “\(x\ne 3\)”是“\(\left| x \right|\ne 3\)”成立的充分条件.
\(④\)“\(A\bigcap B=B\)”是“\(A=\phi \)”的必要不充分条件.
\(⑤\)“若\(a < b\),则\(a+c < b+c\)”的逆否命题是“若\(a+c > b+c\),则\(a > b\)”
判断错误的有___________
已知函数\(y=f(x)\)在\((0,+∞)\)上非负且可导,满足,\(xf′(x)+f(x)\leqslant -x^{2}+x-1\),若\(0 < a < b\),则下列结论正确的是
\((1)\)已知\(-1 < \)\(a\)\( < \)\(b\)\( < 2\),则\(a\)\(-\)\(b\)的范围是__________.
\((2)\)不等式:\(|\)\(x\)\(-1|+2\)\(x\)\( > 4\)的解集是______________.
\((3)\)圆\(C\):\(ρ=-4\)\(\sin \)\(θ\)上的动点\(P\)到直线\(l\):\(ρ\)\(\sin \)\((θ+ \dfrac{π}{4} )= \sqrt{2} \)的最短距离为______.
\((4)\)参数方程\(\begin{cases}x=\cos θ \\ y=1+\cos θ\end{cases} (θ∈R)\)化为普通方程是___________.
若两个函数\(y=f(x)\),\(y=g(x)\)在给定相同的定义域上恒有\(f(x)g(x)\geqslant 0\),则称这两个函数是“和谐函数”\(.\)已知\(f(x)=ax-20\),\(g(x)=\lg (\dfrac{x}{a})(a\in \mathbf{R})\)在\(x∈N^{*}\)上是“和谐函数”,则\(a\)的取值范围是________.
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