During the time interval \( 4 \leq t \leq 16 \), the total number of wolves in a forest can be modeled by the function \( V(t)=-133 \cos \left(0.03 t^{2}\right)+211 \), where \( t \) is measured in weeks. What is the average rate of change in the number of wolves in the forest from time \( t=4 \) to time \( t=16 ? \) You may use a calculator and round to the nearest thousandth. Indicate units of measure.

\( \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 - x ^ { 2 } } } \sqrt { 1 - x ^ { 2 } - y ^ { 2 } } d y d x \)

Pregunta 11 Encuentra la derivada de la \( f(x)=\operatorname{Sen}(3 x) \) \( f^{\prime}(x)=\operatorname{Cos}(3 x) \) \( f^{\prime}(x)=\operatorname{Cos}(x) \) \( f^{\prime}(x)=3 x \operatorname{Cos}(3 x) \) \( f^{\prime}(x)=3 \operatorname{Cos}(3 x) \)

Use one or more definite integrals to find the area between the \( x \)-axis and the given curve on the given interval. Be sure to find if the curve crosses the \( x \)-axis in the given interval. \( f(x)=3-3 x^{2} \) on \( [0,2] \) Area:

\( \iint_{R} d A \), si \( R \) es la región, dada por: \[ R=\left\{(x, y) \in \mathbb{R}^{2}, 0 \leq x \leq \frac{1}{2}, y+x \leq 1, y \geq 0 .\right\} \]

\( \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 - x ^ { 2 } } } \sqrt { 1 - x ^ { 2 } - y ^ { 2 } } d y d x \)