Los intervalos de crecimiento de la función \( f(x)=2 x^{3}-3 x^{2}+12 x+7 \), son: a. \( (-\infty,-2) \cup(1, x) \) b. \( (-\infty,-2) \cup(2, \infty) \) c. \( (-\infty,-1) \cup(2, \infty) \) d. \( (-1,2) \cup(2, \infty) \)

Find the exact area inside one petal of the rose. \( r=6 \sin (4 \theta) \) Area \( =\square \) units \( ^{2} \)

Determine whether the integral is convergent or divergent. If it is convergent, el Round to two decimal places, if necessary. \( \int_{2}^{\infty} \frac{\ln (x)}{x} d x \) Convergent: Divergent

Find the limit of the sequence as \( n \) approaches infinity. \( a_{n}=\frac{8 n-4}{5 n+5} \)

Question 3 ( 4 points) For the following exercises, use this scenario: A pot of boiling soup with an internal temperature of \( 191^{\circ} \) Fahrenheit was taken off the stove to cool in a \( 66^{\circ} \mathrm{Froom} \). After 16 minutes, the internal temperature of the soup was \( 94^{\circ} \mathrm{F} \), how long will it take the soup models this situation too cool to \( 79^{\circ} \mathrm{F} \) ? (round to 2 decimal place) Your Answer:

Does the series \( -\frac{3}{2}+\frac{9}{8}-\frac{27}{32}+\cdots \) converge? If so, find the sum. Converges to: Diverges