Part 2 of 5 A campground owner has 2500 m of fencing. He wants to enclose a rectangular field bordering a river, with no fencing along the river. (See the s 0.71 of 1 (a) Write an expression for the length of the field as a function of \( x \). (b) Find the area of the field (area \( = \) length \( \times \) width) as a function of \( x \). (c) Find the value of \( x \) leading to the maximum area. (d) Find the maximum area. (a) \( \ell(x)=2500-2 x \) (b) \( A(x)= \)

State the equation of \( f(x) \) if its domain is \( \{x \in R \mid x \neq 0\} \), the \( y \)-intercept does not exist, and the equation of the horizontal asymptote is \( y=1 \).

A weight attached to a spring is at its lowest point, 9 inches below equilibrium, at time \( t=0 \) seconds. When the weight it released, it oscillates and returns to its original position at \( t=3 \) seconds. Which of the following equations models the distance, \( d \), of the weight from its equilibrium after \( t \) seconds? \( d=-9 \cos \left(\frac{\pi}{3} t\right) \) \( d=-9 \cos \left(\frac{2 \pi}{3} t\right) \) \( d=-3 \cos \left(\frac{\pi}{9} t\right) \) \( d=-3 \cos \left(\frac{2 \pi}{9} t\right) \)

What is the range of \( y=-5 \sin (x) \) ? all real numbers \( -5 \leq y \leq 5 \) all real numbers \( -\frac{5}{2} \leq y \leq \frac{5}{2} \) all real numbers \( -1 \leq y \leq 1 \) all real numbers \( -\frac{1}{5} \leq y \leq \frac{1}{5} \)

Find Domain of the following: \( h(x)=\frac{x}{\ln x} \) A) \( R \) B) \( R-\{0\} \) C) \( ] 0, \infty[ \) D) \( ] 0,1[U] 1, \infty[ \)

e domain of the function \( f: f(x)=\sqrt{16-x^{2}} \)