4.2 Critically highlight the five-stage model of group development including approaches that can be applied to effectively manage each stage in the model. (15)

1. Determine el límite de cada función, si el límite NO EXISTE, elimine la discontinuidad \[ \begin{array}{l}\text { a. } \lim _{x \rightarrow 2}\left(\frac{x^{3}-8}{x-2}\right)= \\ \text { b. } \lim _{x \rightarrow 4}\left(\frac{x+2}{\sqrt{x}-2}\right)=\end{array} \]

\( \frac { \lim } { x > \frac { 2 } { 3 } } \frac { \sqrt[ 3 ] { \frac { 4 } { 4 } \frac { 2 } { 3 } } } { \frac { 2 } { 5 } x - \frac { 1 } { 6 } } \)

There were 40 people at a party. Each adult ate 5 pies and each child ate 3 pies. The adults ate 128 more pies than the children. (a) How many adults were there at the party? (b) How many pies were eaten by the children?

27. Divida \( P(x)=2 x^{3}-9 x^{2}+3 x-6 \) por \( H(x)=x-2 \) pelo mé- todo da chave. a) Qual é o resto dessa divisão?

Use principle of Mathematical Induction to prove that: \[ \frac{1}{1 * 2}+\frac{1}{2 * 3}+\ldots \ldots \ldots \ldots+\frac{1}{n(n+1)}=\frac{n}{n+1} \]