47) \( f(x)=3 x^{3}-5 x^{2}+15 x-25 \) A) \( \left\{-\frac{7}{3}, i \sqrt{5},-i \sqrt{5}\right\} \) B) \( \left\{\frac{5}{3}, i \sqrt{6},-i \sqrt{6}\right\} \) C) \( \left\{\frac{5}{3}, \frac{i \sqrt{10}}{2},-\frac{i \sqrt{10}}{2}\right\} \) D) \( \left\{\frac{5}{3}, i \sqrt{5},-i \sqrt{5}\right\} \)

Consider the curve defined by the given parametric equations. \( \left\{\begin{array}{l}x=-5+\sec (t) \\ y=-4+2 \tan (t)\end{array}\right. \) Find the first derivative (in terms of \( t \) ). \( \frac{d y}{d x}= \) Find the second derivative (in terms of \( t \) ). \( \frac{d^{2} y}{d x^{2}}= \) Determine whether the curve is concave up or concave down at \( t= \) Concave down Concave up

Evaluate the limit with either L'Hôpital's rule or previously learned m \( \lim _{x \rightarrow \frac{\pi}{2}} \frac{\cos (x)}{\frac{\pi}{2}-x}=\square \)

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

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

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 \( 66^{\circ} \mathrm{F} \) room. 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)