The motion of a particle performing damped vibrations is given by \( \gamma=e^{-t} \operatorname{Sin} 2 t, \gamma \) being the displacement trom its mean position at time \( t \). Show that \( \gamma \) is a maximum when \( t=1 / 2 \tan ^{-1}(2) \) and determine this maximum displacement to three significant figures.

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

\( x^{3}-x-4=0 \) in the interval. (1,2) in 10 iterations.

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

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

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