y=(x^2+x+1)/x

Frequently Asked Questions

• 求导数 \(y=(x^2+x+1)/x\)

  

  $$y^{\prime }=\frac{x^2-1}{x^2}$$

• 查找域 \(y=(x^2+x+1)/x\)

  

  $$x\ne 0$$

• $$\text{找到 }x\text{ 截距/零}$$ \(y=(x^2+x+1)/x\)

  

  $$\text{No x-intercept}$$

• 找到 y 轴截距 \(y=(x^2+x+1)/x\)

  

  $$\text{No y-intercept}$$

• 找到临界点 \(y=(x^2+x+1)/x\)

  

  $$\begin{array}{rl}& x=1\\ & x=-1\end{array}$$

• 找到局部极值 \(y=(x^2+x+1)/x\)

  

  $$\begin{array}{rl}& \text{The local minimum is}3\text{at}x=1\\ & \text{The local maximum is}-1\text{at}x=-1\end{array}$$

• 查找递增或递减区间 \(y=(x^2+x+1)/x\)

  

  $$\begin{array}{rl}& \text{The increasing interval is}x\in \left(-\infty ,-1\right]\cup \left[1,+\infty \right)\\ & \text{The decreasing interval is}x\in \left[-1,0\right)\cup \left(0,1\right]\end{array}$$

• 查找范围 \(y=(x^2+x+1)/x\)

  

  $$y\in \left(-\infty ,-1\right]\cup \left[3,+\infty \right)$$

• 找到垂直渐近线 \(y=(x^2+x+1)/x\)

  

  $$\begin{array}{rl}& x=0\end{array}$$

• 找到水平渐近线 \(y=(x^2+x+1)/x\)

  

  $$\text{No horizontal asymptotes}$$

• 找到斜渐近线 \(y=(x^2+x+1)/x\)

  

  $$y=x+1$$

• 确定是偶数、奇数还是两者都不是 \(y=(x^2+x+1)/x\)

  

  $$\text{Neither even nor odd}$$

• 求驻点 \(y=(x^2+x+1)/x\)

  

  $$\left(-1,-1\right),\left(1,3\right)$$

• 找到拐点 \(y=(x^2+x+1)/x\)

  

  $$\text{No inflection points}$$

• 测试关于原点的对称性 \(y=(x^2+x+1)/x\)

  

  $$\text{Not symmetry with respect to the origin}$$

• 测试关于 x 轴的对称性 \(y=(x^2+x+1)/x\)

  

  $$\text{Not symmetry with respect to the x-axis}$$

• 测试关于 y 轴的对称性 \(y=(x^2+x+1)/x\)

  

  $$\text{Not symmetry with respect to the y-axis}$$

• $$\text{求解 }y$$ \(y=(x^2+x+1)/x\)

  

  $$y=\frac{x^2+x+1}{x}$$

• 以极坐标形式重写 \(y=(x^2+x+1)/x\)

  

  $$\begin{array}{rl}& r=\frac{\cos \left(\theta \right)+\sqrt{-3{\cos }^2\left(\theta \right)+2\sin \left(2\theta \right)}}{\sin \left(2\theta \right)-2{\cos }^2\left(\theta \right)}\\ & r=\frac{\cos \left(\theta \right)-\sqrt{-3{\cos }^2\left(\theta \right)+2\sin \left(2\theta \right)}}{\sin \left(2\theta \right)-2{\cos }^2\left(\theta \right)}\end{array}$$