\begin{tabular}{l} Question \\ Use Newton's method to approximate the solution to the equation \( 7 \cos (x)=3 x+1 \). Use \( x_{0}=2 \) as your starting value \\ to find the approximation \( x_{2} \) rounded to the nearest thousandth. \\ Provide your answer below: \\ \\ \( x_{2} \approx \square \) \\ \hline\end{tabular}

5. [12 marks] Using calculus and showing all your working, sketch the function \[ f(x)=\frac{x}{x^{2}-4} \] noting the domain of \( f(x) \), any intercepts or asymptotes, symmetry, regions where the function is increasing or decreasing and any relative extrema. Note: You don't have to consider the second derivative and concavity.

\( ( e ^ { x } - \sin y ) d x + ( \cos y ) d y \)

s] Using calculus and showing all working, graph the function \[ f(x)=\frac{x+2}{x^{2}-1} \]

Decide whether the following statement is true or false. The cube function is odd and is increasing on the interval \( (-\infty, \infty) \). Choose the correct answer below. False True

\( \lim _ { n \rightarrow + \infty } \frac { n ^ { 5 } + \sin n } { 3 ( \arctan n ) n ^ { 5 } } \)