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

\( \left. \begin{array} { l } { u = x ^ { 2 } + 3 x + 2 \quad u ^ { \prime } = 2 x + 3 } \\ { V = x - 1 \quad V ^ { \prime } = 1 } \\ { \frac { ( 2 x + 3 ) ( x - 7 ) - ( x ^ { 2 } + 3 x + 2 ) ( 1 ) } { ( x - 1 ) ^ { 2 } } } \end{array} \right. \)

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

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

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

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