Chapter 5

For the following exercises, identify the removable discontinuity. $$ f(x)=\frac{2 x^{2}+5 x-3}{x+3} $$

For the following exercises, find the dimensions of the right circular cylinder described. The radius and height differ by one meter. The radius is larger and the volume is \(48 \pi\) cubic meters.

For the following exercises, write the polynomial function that models the given situation. A cylinder has a radius of \(x+2\) units and a height of 3 units greater. Express the volume of the cylinder as a polynomial function.

For the following exercises, identify the removable discontinuity. $$ f(x)=\frac{x^{3}+x^{2}}{x+1} $$

For the following exercises, find the dimensions of the right circular cylinder described. The radius and height differ by two meters. The height is greater and the volume is \(28.125 \pi\) cubic meters.

For the following exercises, write the polynomial function that models the given situation. A right circular cone has a radius of \(3 x+6\) and a height 3 units less. Express the volume of the cone as a polynomial function. The volume of a cone is \(V=\frac{1}{3} \pi r^{2} h\) for radius \(r\) and height \(h\).

For the following exercises, express a rational function that describes the situation. A large mixing tank currently contains 200 gallons of water, into which 10 pounds of sugar have been mixed. A tap will open, pouring 10 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 3 pounds per minute. Find the concentration (pounds per gallon) of sugar in the tank after \(t\) minutes.

For the following exercises, find the dimensions of the right circular cylinder described. The radius is \(\frac{1}{3}\) meter greater than the height. The volume is \(\frac{98}{9} \pi\) cubic meters.

For the following exercises, express a rational function that describes the situation. A large mixing tank currently contains 300 gallons of water, into which 8 pounds of sugar have been mixed. A tap will open, pouring 20 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 2 pounds per minute. Find the concentration (pounds per gallon) of sugar in the tank after \(t\) minutes.

For the following exercises, express a rational function that describes the situation. The concentration \(C\) of a drug in a patient's bloodstream \(t\) hours after injection is given by \(C(t)=\frac{2 t}{3+t^{2}}\). What happens to the concentration of the drug as \(t\) increases?

For the following exercises, express a rational function that describes the situation. The concentration \(C\) of a drug in a patient's bloodstream \(_{t}\) hours after injection is given by \(C(t)=\frac{100 t}{2 t^{2}+75} .\) Use a calculator to approximate the time when the concentration is highest.

For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator to answer the question. An open box with a square base is to have a volume of 108 cubic inches. Find the dimensions of the box that will have minimum surface area. Let \(x=\) length of the side of the base.

For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator to answer the question. A rectangular box with a square base is to have a volume of 20 cubic feet. The material for the base costs 30 cents/ square foot. The material for the sides costs 10 cents/square foot. The material for the top costs 20 cents/square foot. Determine the dimensions that will yield minimum cost. Let \(x=\) length of the side of the base.

For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator to answer the question. A right circular cylinder has volume of 100 cubic inches. Find the radius and height that will yield minimum surface area. Let \(x=\) radius.A right circular cylinder has volume of 100 cubic inches. Find the radius and height that will yield minimum surface area. Let \(x=\) radius.

For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator to answer the question. A right circular cylinder with no top has a volume of 50 cubic meters. Find the radius that will yield minimum surface area. Let \(x=\) radius.

For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator to answer the question. A right circular cylinder is to have a volume of 40 cubic inches. It costs 4 cents/square inch to construct the top and bottom and 1 cent/square inch to construct the rest of the cylinder. Find the radius to yield minimum cost. Let \(x=\) radius.