¿Cuál es la razón de cambio del volumen de una caja cúbica cuando el lado de la caja está incrementando a una tasa de \( 0.5 \mathrm{~cm} / \mathrm{s} \) y el lado es de 10 cm ? \( \begin{array}{ll}\text { a) } 100 \mathrm{~cm}^{3} / \mathrm{s} & \text { b) } 150 \mathrm{~cm}^{3} / \mathrm{s} \\ \text { c) } 250 \mathrm{~cm}^{3} / \mathrm{s} & \text { d) } 200 \mathrm{~cm}^{3} / \mathrm{s}\end{array} \)

(v) The value of \( \int_{-\infty}^{\infty} \delta(t) d t \) is: (a) 0 (b) 1 (c) -1 (d) \( \infty \) (vi) Solution of \( \frac{d^{2} x}{d x^{2}}-k x=0 \), when \( k=0 \) is: (a) \( c_{1} x+c_{2} \) (b) \( c_{1} \cos x+c_{2} \sin x \) (c) \( c_{1} e^{\lambda x}+c_{2} e^{-\lambda x} \) (d) None of these (vii) Equation \( u_{t u}-c^{2} u_{x z}=0 \) is: (a) one dimensional wave equation P.T.O.

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.

50. Determinaţi valorile parametrului real \( m \) pentru care graficul funcțici \( f: R \rightarrow R \), \( f(x)=\sqrt[3]{x^{2}+m x+1} \) are tangentă in fiecare punct \( x \in R \).

\( \int ( 2 x + 3 ) ^ { 2 } \sqrt[ 3 ] { x - 2 } \)

The function \( f(x)=\frac{x}{x+1} \) is concave up on