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 \( (3 ; \pi / 2 ; 18) \)

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

\( y = ( 4 x ^ { 2 } - 2 x + 6 ) ( x ^ { 2 } + 6 x - 3 ) \quad y ^ { \prime } = \)

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

1) \( y=3 x^{3}-6 x^{3}+11 x-8 x^{2} \) 2) \( y=-4 x^{-\frac{2}{3}}-8 x^{-\frac{3}{4}}+4 x^{-3}+5 x \) 3) \( y=6 x^{-\frac{1}{2}}+8 x^{-\frac{3}{4}}-6 x^{-1}-4 x^{-3} \)

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