3. If \( f(x)=\frac{2 x}{x-3} \), compute \( \frac{f(a+h)-f(a)}{h} \) and simplify.

\begin{tabular}{l} Exercice 2: \\ Soit \( f \) la fonction numérique définie sur l'intervalle \( I=[0 ; 1] \) par : \( f(x)=4 x \sqrt{x}-3 x^{2} \) \\ 1- Montrer que \( f \) est croissante sur \( I \) \\ 2- On considère la suite \( \left(u_{n}\right) \) définie par : \( u_{0}=\frac{4}{9} \) et \( (\forall n \in \mathbb{N}) u_{n+1}=4 u_{n} \sqrt{u_{n}}-3 u_{n}^{2} \) \\ a- Montrer que \( (\forall n \in \mathbb{N}) \frac{4}{9} \leq u_{n} \leq 1 \) \\ b- Montrer que \( \left(u_{n}\right) \) est croissante. \\ c- En déduire que \( \left(u_{n}\right) \) est convergente et calculer \( \lim _{n \rightarrow+\infty} u_{n} \) \\ \hline Exercice 3: \end{tabular}

\( x = \theta \sin \theta + \cos \theta , y = \sin \theta - \theta \cos \theta \)

\( \int _{}^{}\frac{1}{x\sqrt {4x^{2}+4x+3}} d x \)

10) A bucket of uranium ore decays at a rate of \( -0.34 \% \) per year. If the bucket has 3 kgs of uranium at the start, how long will take for the bucket to decay to 1 kg ?

2. Find the largest interval in which \( p^{*} \) must lie to approximate \( p \) with relative error at most \( 10^{-4} \) for each value of \( p \). \( \begin{array}{ll}\text { a. } \pi & \text { b. } e \\ \text { c. } \sqrt{2} & \text { d. } \sqrt[3]{7}\end{array} \) 3. Suppose \( p^{*} \) must approximate \( p \) with relative error at most \( 10^{-3} \). Find the largest interval in which \( p^{*} \) must lie for each value of \( p \). \( \begin{array}{ll}\text { a. } 150 & \text { b. } 900 \\ \text { c. } 1500 & \text { d. } 90\end{array} \)