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

Frequently Asked Questions

• Calcule a derivada \(y=(x^2+x+1)/x\)

  

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

• Encontre o domínio \(y=(x^2+x+1)/x\)

  

  $$x\ne 0$$

• $$\text{Encontre a interceptac¸a˜o }x\text{ / zero}$$ \(y=(x^2+x+1)/x\)

  

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

• Encontre a interceptação y \(y=(x^2+x+1)/x\)

  

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

• Encontre os números críticos \(y=(x^2+x+1)/x\)

  

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

• Encontre os extremos locais \(y=(x^2+x+1)/x\)

  

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

• Encontre o intervalo crescente ou decrescente \(y=(x^2+x+1)/x\)

  

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

• Encontre o alcance \(y=(x^2+x+1)/x\)

  

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

• Encontre as assíntotas verticais \(y=(x^2+x+1)/x\)

  

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

• Encontre as assíntotas horizontais \(y=(x^2+x+1)/x\)

  

  $$\text{No horizontal asymptotes}$$

• Encontre as assíntotas oblíquas \(y=(x^2+x+1)/x\)

  

  $$y=x+1$$

• Determine se é par, ímpar ou nenhum \(y=(x^2+x+1)/x\)

  

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

• Encontre os pontos estacionários \(y=(x^2+x+1)/x\)

  

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

• Encontre os pontos de inflexão \(y=(x^2+x+1)/x\)

  

  $$\text{No inflection points}$$

• Teste de simetria sobre a origem \(y=(x^2+x+1)/x\)

  

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

• Testando a simetria em torno do eixo x \(y=(x^2+x+1)/x\)

  

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

• Testando a simetria sobre o eixo y \(y=(x^2+x+1)/x\)

  

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

• $$\text{Resolva para }y$$ \(y=(x^2+x+1)/x\)

  

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

• Reescrever na forma polar \(y=(x^2+x+1)/x\)

  

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