14. attending to

The vector field \[ \mathrm{F}(x, y, z)=y z \mathbf{i}+x y^{2} \mathbf{j}+y z^{2} \mathrm{k} \] has divergence and curl

Solve for \( b \). \[ -4 b-16=-2 b+18 \]

Let \( f(x)=\frac{14 x^{4}+a x^{2}+b}{7 x^{4}+c x^{2}+d} \), where \( a, b, c \), and \( d \) are unknown constants. Which of the following is a possible graph of \( y=f(x) \) ? Dashed lines indicate asymptotes.

Compute the difference quotient, \( \frac{f(x+h)-f(x)}{h} \), for the function \( f(x)=6 x^{2}+7 x \), and simplify the answer as much as possible. \( \frac{f(x+h)-f(x)}{h}=\square \)

Se deja caer en un pozo una piedra que en un principio es- tá en reposo. El sonido del chapoteo se escucha exacta- mente 2.00 s después. Determine la profundidad del pozo si la temperatura del aire es de \( 10.0^{\circ} \mathrm{C} \).