16.1-bo'lim : Vektor maydonlari

1. \(\vec F = - {y^2}\,\vec i + x\,\vec j\) uchun vektor maydonini chizing.
2. \(\vec F = \,\vec i + xy\,\vec j\) uchun vektor maydonini chizing.
3. \(\vec F = \,4y\,\vec i + \left( {x + 2} \right)\vec j\) uchun vektor maydonini chizing.
4. \(f\left( {x,y} \right) = 6{x^2} - 9y + {x^3}\,\sqrt y \) uchun gradient vektor maydonini hisoblang.
5. \(f\left( {x,y} \right) = \sin \left( {2x} \right)\cos \left( {3x} \right)\) uchun gradient vektor maydonini hisoblang.
6. \(f\left( {x,y,z} \right) = z\,{{\bf{e}}^{x\,y}} + {y^3}\tan \left( {4x} \right)\) uchun gradient vektor maydonini hisoblang.
7. \(f\left( {x,y,z} \right) = x\,{y^2}{z^3} + 4x{{\bf{e}}^{{y^{\,2}}}} - \ln \left( {x - z} \right)\) uchun gradient vektor maydonini hisoblang.