共50条信息
设函数\(f(x)={{(x-a)}^{2}}+{{(2\ln x-2a)}^{2}}\),其中\(x > 0,a\in {R}\),存在\({{x}_{0}}\)使得\(f({{x}_{0}})\leqslant \dfrac{4}{5}\)成立,则实数\(a\)的值是\((\) \()\)
在函数\(f(x)=-{{e}^{x}}-x\)的图象上任意一点处的切线为\({{l}_{1}}\),若总存在函数\(g(x)=ax+2\cos x\)的图象上一点,使得在该点处的切线\({{l}_{2}}\)满足\({{l}_{1}}\bot {{l}_{2}}\),则\(a\)的取值范围是( )
已知倾斜角为\(\theta \)的直线\(l\)与直线垂直,则\(\sin 2\theta =(\) \()\)
设曲线\(y= \dfrac{x+1}{x-1} \)在点\(\left(3,2\right) \)处的切线与直线\(ax+y+3=0\)垂直,则\(a=\) ( )
已知直线\({{l}_{1}}:mx-y+3=0\)与\({{l}_{2}}\)关于直线\(y=x\)对称,\({{l}_{2}}\)与\({{l}_{3}}:y=-\dfrac{1}{2}x+\dfrac{1}{2}\)垂直,则\(m=(\) \()\)
过圆\({{x}^{2}} +{{y}^{2}}-4x=0\)外一点\(P(m,n)\)作圆的两条切线,当这两条切线互相垂直时,\(m\),\(n\)应满足的关系式为( )
设曲线\(y= \dfrac{x+1}{x-1} \)在点\(\left(3,2\right) \)处的切线与直线\(ax+y+1=0 \)垂直,则\(a=(\) \()\)
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