A certain tranquilizer decays exponentially in the bloodstrean and has a half-life of 22 hours. How long with it take for the drug to decuy to \( 82 \% \) of the original dose? a) step 1 : Find K (Round to four decinal pleces) b) step \( 2: \) Use \( k \) to determine how longlinhours) it will take for the devg to decay to \( 82 \% \) of the original dose. (Round to one decinalplace)

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

asymptotes of \( f \).

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

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.

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.