Find the domain of the function $f(x)=arctanx$

A$.(-7,8)$

B$.|-1,1|$

C$.(-,)$

D$.0,$

E$.\{\}$

The graph of a function $f$ consists of a semicircle and two line segments as shown. Let $g(x)={\displaystyle \underset{1}{\overset{x}{}}}f(t)dt.$ Answer the questions $15-17$ according to the figure below.

Find $g(3)$

A$.-2$

B$.-1$

C$.0$

D$.1$

E$.\frac{1}{2}$

Find all values of $x$ on the open interval $(-3,4)$ at which $g$ has a relative maximum.

A$.x=4,$ B$.x=3$

C$.x=2$

D$.x=1$

E$.x=-1$

Find the $x-$coordinate of each point of inflection of the graph of $g$ on the open interval $(-3,4).$

A$.x=-1,x=2$

B$.x=1$

C$.x=2$

D$.x=3$

E$.g$ has no inflection point

The graph of the derivative of $h(z)$ is aits.

Which of the following conld be the graph of $h(x)?$

A farmer has $80m$ of fence to enclose a rectangular area against a straight river. He only needs to fence in three sides. What is the maximum area $($in $m^2)$ that be can endose with his materials?

A$.160$

B$.320$

C$.960$

D$.3200$

E$.$ None How fast $($in cm$/$s$)$ is the rafirs imcressing thum the mains of the ballocm is $10cm?$

A$.\frac{1}{?}=$

B$.\frac{2}{x}$

c$.\frac{1}{2x}$

D$.\frac{1}{3x}+-\frac{1}{3x}$