A population of bacteria grows at a rate of \( \mathrm{P}^{\prime}(t)=30 e^{\mathrm{t}} \), where \( t \) is time in hours. Determine how much the population increases from \( \mathrm{t}=0 \) to \( t=3 \). Round your answer to two decimal places. A. 572.57 B. 602.57 C. \( 1,175.14 \) D. 587.57

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.

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

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.

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

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