Pregunta: 8. F(x, y) = (2xy + y 2)i + (x² - 2xy-3) j, y>0 C F • 1 Quain (a (

8. $\mathbf{F}(x,y)=\left(2xy+y^{-2}\right)\mathbf{i}+\left(x^2-2x{y}^{-3}\right)\mathbf{j},y>0$ 3-10 Determine whether or not $\mathbf{F}$ is a conservative vector field. If it is, find a function $f$ such that $\mathbf{F}=\nabla f$. 3. $\mathbf{F}(x,y)=\left(xy+y^2\right)\mathbf{i}+\left(x^2+2xy\right)\mathbf{j}$ 4. $\mathbf{F}(x,y)=\left(y^2-2x\right)\mathbf{i}+2xy\mathbf{j}$ 5. $\mathbf{F}(x,y)=y^2{e}^{xy}\mathbf{i}+(1+xy)e^{xy}\mathbf{j}$ 6. $\mathbf{F}(x,y)=y{e}^x\mathbf{i}+\left(e^x+e^y\right)\mathbf{j}$ 7. $\mathbf{F}(x,y)=\left(y{e}^x+\sin y\right)\mathbf{i}+\left(e^x+x\cos y\right)\mathbf{j}$ 8. $\mathbf{F}(x,y)=\left(2xy+y^{-2}\right)\mathbf{i}+\left(x^2-2x{y}^{-3}\right)\mathbf{j},y>0$ 9. $\mathbf{F}(x,y)=\left(y^2\cos x+\cos y\right)\mathbf{i}+(2y\sin x-x\sin y)\mathbf{j}$ 10. $\mathbf{F}(x,y)=(\ln y+y/x)\mathbf{i}+(\ln x+x/y)\mathbf{j}$