\begin{tabular}{l} Question \\ Given the cost function \\ \( \qquad C(x)=2800+550 x+0.4 x^{2} \) \\ and the demand function \( p(x)=1870 \) for each item \( x \), find the production level \( x \) that will maximize profit. Your answer \\ should be the whole number that corresponds to the highest profit. \\ Provide your answer below: \\ \( \qquad \begin{array}{l}\text { P items }\end{array} \) \\ \hline\end{tabular}

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

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

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.

MAS182 - Applied Mathematics 13. Final Examination - S1 2021 The water content \( W(t) \) (measured in grams) in the cheese is governed by the differential equation \[ \frac{d W}{d t}=-(W-100)^{2} \] with initial condition \( W(0)=200 \mathrm{~g} \) and time is measured in hours.