解析 B正确率: 46%, 易错项: C 解:原式=\left( \frac{x}{x}+\frac{1}{x} \right)\div \frac{{{\left( x+1 \right)}^{2}}}{x}=\frac{\left( x+1 \right)}{x}\cdot \frac{x}{{{\left( x+1 \right)}^{2}}}=\frac{1}{x+1}.故选:B....
【解析】[x]表示不超过x的最大整数 则$$ [ x ] \in [ x , x + 1 $$要利用这个性质 则有: , $$ x + \frac { x } { 2 } - 1 + \frac { x } { 6 } - 1 + \frac { x } { 1 0 } - 1 \leq \left[ \frac { x } { 1 } \right] \\ + \left[ \frac {...
f(x)=h(g(x)) fʼ(x)=hʼ(g(x))gʼ(x)=3(g(x))²(2x)=3(x²+1)²(2x)=6x(x²+1)². 积分 复合函数 三角函数与圆 可微函数 平方根 更多相关概念 来自Web 搜索的类似问题 How do you solve x−53=1 ? https://socra...
15.已知f(x)=$\left\{{\begin{array}{l}{\frac{1}{{f}}-1.-1<x<0}\\{x.0≤x<1}\end{array}}$.若方程f有唯一解.则实数a的取值范围是( )A.$[{\frac{1}{3}.+∞})$B.$[{\frac{1}{5}.+∞})$C.$\left\{1\right\}∪[{\frac{1}{3}.+∞})$D.$\left\{{-1}\right\}...
f\left( 2 \right)+f\left( \frac{1}{2} \right)=\frac{1}{1+2}+\frac{1}{1+\dfrac{1}{2}}=\frac{1}{3}+\frac{2}{3}=1,f\left( 3 \right)+f\left( \frac{1}{3} \right)=\frac{1}{1+3}+\frac{1}{1+\dfrac{1}{3}}=\frac{1}{4}+\frac{3}{4}=1,\vdo...
由题意:函数f\left( x \right)=\frac{1-{{2}^{x}}}{a+{{2}^{x+1}}}是奇函数.∴f\left( -x \right)+f\left( x \right)=0.即\frac{1-{{2}^{-x}}}{a+{{2}^{1-x}}}+\frac{1-{{2}^{x}}}{a+{{2}^{x+1}}}=0,化简整理得:\frac{{{2}^{x}}-1}{...
所以{{f}^{\prime }}\left( 1 \right)=-1,f\left( 1 \right)=-1,即切线方程:y=-x,下证:\frac{1}{2}{{x}^{2}}+2x\ln x-4x+\frac{5}{2}\geqslant -x,令\varphi \left( x \right)=\frac{1}{2}{{x}^{2}}+2x\ln x-3x+\frac{5}{2},...
【解析】 解:由于 $$ \lim _ { x \rightarrow 0 } \left[ \frac { 1 } { x } - ( \frac { 1 } { x } - a ) e ^ { x } \right] = \lim _ { x \rightarrow 0 } \frac { 1 - ( 1 - a x ) e ^ { x } } { x } \\ = \lim _ { x \rightarrow 0 } ...
【解析】 $$ \lim _ { x \rightarrow 0 } \left[ \frac { 1 } { \ln ( 1 + x ) } - \frac { 1 } { x } \right] = \lim _ { x \rightarrow 0 } \frac { x - \ln ( 1 + x ) } { x \ln ( 1 + x ) } = \lim _ { x \rightarrow 0 } \frac { x...
a\leqslant 0时,{{f}^{\prime }}\left( x \right) < 0,f\left( x \right)的单调递减区间为:(0,+\infty ),a>0时,f\left( x \right)在\left( 0,\frac{\sqrt{a}}{a} \right)递减,在(\frac{\sqrt{a}}{a},+\infty )递增. ∵ (f^(' ))( x )=ax-1/x=(a(x^2)-1...