Diberikan medan vektor umum \( A=4 r^{2} z^{2} \hat{a}_{r}+6 r \sin \varphi \hat{a}_{\varphi}+5 z^{3} r \hat{a}_{z} \) dalam koordinat silinder Carilah curl A dititik \( (3 ; \pi / 2 ; 18) \)

1) Hallar los puntor sobre el grafica de \( x^{2}+4 x y+y^{2}=4 \) donde Cla recta tangente es Horizontal

\( \left\{\begin{array}{l}f(x)=x^{2}-1 \\a=1 \\\lim _{h \rightarrow 0} (\frac{f(a+h-f(a)}{h}\end{array}\right. \)

1) \( y=3 x^{3}-6 x^{\frac{5}{3}}+11 x-8 x^{\frac{3}{2}} \) 2

implications. 10. Deseribe how vector calculas is utilized in electromagnetiom, specif- eally in calculating electric flelds.

\( \left. \begin{array} { l l } { u = x ^ { 2 } + 3 x + 2 } & { u ^ { \prime } = 2 x + 3 } \\ { v = x - 1 } & { v ^ { 3 } = 1 } \\ { } & { ( 2 x + 3 ) ( x - 1 ) - ( x ^ { 2 } + 3 x ) 2 ) ( 1 ) } \end{array} \right. \)