Al calcular el \( \lim _{x \mapsto 0} \frac{\ln \left(1+\frac{x}{3}\right)}{x} \) se obtiene: \( \begin{array}{l}\text { a. }-1 / 3 \\ \text { b. } 1 / 3 \\ \text { c. } 3 \\ \text { d. }-3\end{array} \)

valuar las siguientes i \( \int \sqrt{3-2 x} x^{2} d x \)

\( \int _ { 0 } ^ { 45 } \sec ^ { 4 } x d x \)

\( \begin{aligned} \text { 40. } y=\frac{b}{a} \sqrt{a^{2}-x^{2}} & \frac{d y}{d x} & =-\frac{b^{2} x}{d^{2} y} \\ \text { H. } y=\left(a^{2 / 3}-x^{2 / 3}\right)^{3 / 3} & \frac{d y}{d x} & =-\sqrt[3]{\frac{y}{x}}\end{aligned} \)

Un agricultor necesita calcular el área bajo la curva de una función que representa tasa de crecimiento de sus cultivos, \( g(t)=t 3-t \), en el intervalo d tiempo \( [0,2] \). El área bajo la curva de la función \( g(t) \) en ese intervalo es a. 10 b. 8 c. 4 d. 6

Sociologists have found that crime rates are influenced by temperature. In a town of 100,000 people, the crime rate has been approximated as \( \mathrm{C}=\frac{1}{10}(\mathrm{~T}-60)^{2}+100 \), where C is the humber of crimes per month and \( T \) is the average monthly temperature in degrees Fahrenheit. The average temperature for May was \( 72^{\circ} \) and by the end of May the temperature was rising at the rate of \( 7^{\circ} \) per month. How fast is the crime rate rising at the end of May? At the end of May, the crime rate is rising by (Simplify your answer.)