共50条信息
已知函数\(f(x)={{{e}}^{ax}}\cdot \sin x-1\),其中\(a > 0\).
\((\)Ⅰ\()\)当\(a=1\)时,求曲线\(y=f(x)\)在点\((0,f(0))\)处的切线方程;
\((\)Ⅱ\()\)证明:\(f(x)\)在区间\([0,{ }\!\!\pi\!\!{ }]\)上恰有\(2\)个零点.
已知函数\(f(x)=2x\ln x+{{x}^{2}}-mx+3\),在定义域内\(f(x)\geqslant 0\)恒成立,则实数\(m\)的取值范围是\((\) \()\)
设\(f\left( x \right)=x\ln \ x\),若\({f}{{{"}}}\left( {{x}_{0}} \right)=2\),则\({{x}_{0}}\)等于\((\) \()\)
设\(f(x)=e^{x}(x+2x)\),令\(f_{1}(x)=f{{"}}(x)\),\(f_{n+1}(x)=f_{n}{{"}}(x)\),若\(f_{n}(x)=e^{x}(A_{n}x^{2}+B_{n}x+C_{n})\),则数列\(\left\{ \dfrac{1}{{{C}_{n}}} \right\}\)前\(n\)项和为\(S_{n}\),当\(|{{S}_{n}}-1|\leqslant \dfrac{1}{2018}\)时,\(n\)的最小整数值为\((\) \()\)
已知\(f\left( x \right)=\dfrac{1}{4}{{x}^{2}}+\sin \left( \dfrac{\pi }{2}+x \right),{f}{{{"}}}\left( x \right)\)为\(f\left( x \right)\)的导函数,则\({f}{{{"}}}\left( x \right)\)的图像是\((\) \()\)
已知\(f(x)={{e}^{-x}}+2f{{{"}}}(0)x\),则\(f{{{"}}}(-1)=(\) \()\)
设函数\(f\left( x \right)={{e}^{x}}\sin \pi x\),则方程\(xf\left( x \right)={f}{{"}}\left( x \right)\)在区间\(\left( -2014,2016 \right)\)上的所有实根之和为( )
若定义在\(R\)上可导函数\(f(x)\)满足\(f(x)+f{{"}}(x) > 2,f(0)=4\)则不等式\({{e}^{x}}f(x) > 2{{e}^{x}}+2(\)其中\(e\)为自然对数的底数\()\)的解集为
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