A scale factor \( \frac{1}{5} \) is applied to a cone with a surface area of 100 units \( { }^{2} \). What will the surface area of the new cone be? (1) What effect does this change have on the volume of the cone? The radius of a sphere is increased from \( r \) to \( 4 r \). (1) What is the scale factor? (2) What is the effect of the surface area? (3) What is the effect on the volume? A sphere has a radius \( r \), surface area \( A \) and volume \( V \). If a scale factor \( \frac{1}{2} \) sphere, express (1) the new radius in terms of \( r \). (2) the new surface area in terms of \( A \). (3) the new volume in terms of \( V \).

h) \( \int \frac{3+6 x+4 x^{2}-2 x^{3}}{x^{2}\left(x^{2}+3\right)} d x \)

Try \( x_{0}=-2 \) for the following differential equation \( y^{\prime \prime}-x y=0 \).

9) At which value of x the function \( f(x)=(x-2)(x-3)^{2} \) has a local \( \begin{array}{lllll}\text { maximum? } & \text { (A) } \frac{-7}{3} & \text { (B) } \frac{-5}{2} & \text { (C) }-3 & \text { (D) } \frac{7}{3}\end{array} \)

\( \lambda \omega ^ { w } = 1 , w _ { 0 } \)

7. Graham recibe \( \$ 690.000 \) al jubilarse. inuen en una renta vitalicia a ucinte años, inmediata con pagos anuales y el resto \& 690.000 - x se utiliza para comprar una perpetuidad inmediata con pagos anuales. Durante los primeros veinte años, los pagos anuales totales que recibe de las dos inucrsiones son el dobl. delo que recibe posteriormente. la tasa de interes eqectiva anual es del \( 5 \% \) halla \( x \).