Question Evaluate the following limit using L'Hospital's rule. \[ \lim _{x \rightarrow 12^{+}}\left[\frac{168}{5 x^{2}-85 x+300}-\frac{2 x}{5 x-60}\right] \] Provide an exact answer.

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.

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

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

1) \( f(x)=\sqrt{\frac{2}{\sqrt[x]{e 6 x+1}}} \)

Gegeben ist eine weitere Funktion h. mit der Gleichung \( h(x)=0,5 x^{3}-4 x^{2}+6 x+2 \) 74 a) Untersuchen Sie den Graphen von \( h \) auf mögliche Wendepunkte.