Math and computer studies teacher.I like Physics, too.
Sketch the region enclosed by the given curves and find its area.$y=e^{x}, \quad y=x e^{x}, \quad x=0$
Logistic growth A population is modeled by the differential equation$$\frac{d N}{d t}=1.2 N\left(1-\frac{N}{4200}\right)$$where $N(t)$ is the number of individuals at time $t$ (measured in days).(a) For what values of $N$ is the population increasing?(b) For what values of $N$ is the population decreasing?(c) What are the equilibrium solutions?
Let $f(x)=x-3, \quad g(x)=\sqrt{x}, \quad h(x)=x^{3},$ and $j(x)=2 x .$ Express each of the functions in Exercises 11 and 12 as a composite involving one or more of $f, g, h,$ and $j$.a. $y=\sqrt{x}-3$ b. $y=2 \sqrt{x}$c. $y=x^{1 / 4} \quad$ d. $y=4 x$e. $y=\sqrt{(x-3)^{3}} \quad$ f. $y=(2 x-6)^{3}$
Let $f(x)=x-3, \quad g(x)=\sqrt{x}, \quad h(x)=x^{3},$ and $j(x)=2 x .$ Express each of the functions in Exercises 11 and 12 as a composite involving one or more of $f, g, h,$ and $j$.a. $y=2 x-3 \quad$ b. $y=x^{3 / 2}$c. $y=x^{9} \quad$ d. $y=x-6$e. $y=2 \sqrt{x-3} \quad$ f. $y=\sqrt{x^{3}-3}$
Copy and complete the following table.$$\begin{array}{lll}{g(x)} & {f(x)} & {(f \circ g)(x)} \\ \hline\end{array}$$a. $x-7 \quad \sqrt{x} \quad$ ?b. $x+2 \quad 3 x$ ?c. $\quad ? \quad \sqrt{x-5} \quad \sqrt{x^{2}-5}$d. $\frac{x}{x-1} \quad \frac{x}{x-1}$ ?e. $\quad ? \quad 1+\frac{1}{x} \quad x$f. $\frac{1}{x} \quad ? \quad x$
Copy and complete the following table.$$\begin{array}{lll}{g(x)} & {f(x)} & {(f \circ g)(x)}\end{array}$$a. $\frac{1}{x-1} \quad {|x|} \quad {?}$b. $\quad ? \quad \frac{x-1}{x} \quad \frac{x}{x+1}$c. $\quad ? \quad \sqrt{x} \quad|x|$d. $\sqrt{x} \quad ? \quad|x|$
