Question Using L'Hospital's rule, determine whether \( f(x) \) or \( g(x) \) given below grows at a faster rate. \[ \begin{array}{l} f(x)=2 x-3 e^{x} \\ g(x)=-4 x^{2}+3 x+2\end{array} \]

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

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.

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

asymptotes of \( f \).

Proporre un esempio di funzione \( g(x) \) tale che \[ \lim _{x \rightarrow+\infty} \frac{g(x)}{3 \log ^{2} x+1}=+\infty \]