Pre-Calculus 11 Practice Midterm 2 Find the \( x \)-intercepts of the following quadratic function: \( y=3 x^{2}-13 x-10 \)

(a) Montrer que \( \left(v_{n}\right) \) est une suite géométrique de raison \( \mathrm{q}=4 \) (b) Écrire \( v_{n} \) puis \( u_{n} \) en fonction de \( n \) C) Calculer en fonction de \( n: S_{n}=\sum_{k=1}^{n} v_{k} \) puis \( T_{n}=\prod_{k=1}^{n} v_{k} \) On considère la suite \( \left(u_{n}\right) \) définie par: \( u_{0}=2 e t(\forall n \in \mathbb{N}) ; u_{n+1}=\sqrt{6+u_{n}} \) 1 Montrer que : \( (\forall n \in \mathbb{N}) ; 1<u_{n}<3 \) 2 Vérifier que \( :(\forall n \in \mathbb{N}) ; 3-u_{n+1}=\frac{1}{3+\sqrt{6+u_{n}}}\left(3-u_{n}\right) \)

QUESTION 4 It is given that the asymptotes of \( f(x)=\frac{6}{x+p}+q \) intersect at \( (4 ; 3) \). \( 4.1 \quad \) Write down the equation of \( f \). \( 4.2 \quad \begin{array}{l}\text { Sketch the graph of } f \text {, clearly showing all the intercepts with the axes and any } \\ \text { asymptotes. }\end{array} \) \( 4.4 \quad \begin{array}{l}g \text { is one of the axes of symmetry of } f \text { and it is a decreasing function. Determine the } \\ \text { equation of } g \text {. } \\ 4.5 \\ (-3 ; 2) \text { is a point on } f \text {. Determine the coordinates of the image of this point after } \\ \text { reflection in } g \text {. }\end{array} \)

(b) Find the angle between \( \overline{\mathbf{a}} \) and \( \overline{\mathbf{b}} \) where \( -6 \bar{a}+2 \bar{b}=2 i+j-8 k \) and \( 2 \bar{a}-\bar{b}=3 i-4 j+k \) (c) show that the line \( \frac{x-1}{2}=\frac{y-2}{-6}=\frac{z-1}{7} \quad \) is parallel to the tangent vector of the

1. Expand \( (1+x)^{\frac{1}{3}} \) in ascending powers of x up to the term \( x^{3} \). By substituting 0.08 for \( x \) in your result. Obtain an approximation value of the cube root of 5 .

Graph, state domain and range: \[ y=-3 \sqrt{x+3}+5 \]