Sketch the given region R and then find its area. R is the region bounded by the curve $y=\frac{1}{x^{2}}$ and the lines y = x and $y=\frac{x}{8}.$

Find the product of (2x - 2) and (x + 1).

For each of the following functions, find and classify any stationary points. Sketch the function, showing all important features. $f(x)=x^{4}-6 x^{2}+8 x-3$

The potential at a point in space has a certain value, which is not zero. Is the electric potential energy the same for every charge that is placed at that point? Give your reasoning.

The registrar’s report at State University includes the following information: Total enrollment—47,348. Enrollment in the Arts and Science College—27.837. Number of males enrolled in Arts and Sciences—12,722. The alumni magazine wants to interview a randomly selected student about the student’s attitude toward university athletics. The registrar’s office makes a random selection and observes the student is enrolled in Arts and Sciences. Find the probability the students is a male.

A 5-oz serving of a Bloody Mary contains 14 g of alcohol and 5 g of carbohydrates, and thus 116 Calories. A 2.5-oz serving of a martini contains 22 g of alcohol and a negligible amount of carbohydrates, and thus 156 Calories. An average person burns 600 Calories per hour while exercising on a cross-country ski machine. Determine how long it will take to burn the calories from one serving of (a) a Bloody Mary and (b) a martini on this cross-country ski machine.

Choose the word or phrase that best answers the question. What type of compounds form the DNA molecule? A) amino acids B) nucleotides C) polymers D) carbohydrates

Perform the division.

$$\frac { x ^ { 5 } + 3 x + 2 } { x ^ { 3 } + 1 + 2 x }$$

Use an area argument to show that $\ln 2<1$.

Evaluate the expression.

$$5 !$$

Solve each equation.

$$3.2 n = 27.52$$

Describe the positions of the sun, Earth, and the moon during a full moon and during a quarter phase.

Find the vertical asymptotes (if any) of the graph of the function.

$$f(x)=\frac{e^{-2 x}}{x-1}$$

A speedboat moving at 30.0 m/s approaches a no-wake buoy marker 100 m ahead. The pilot slows the boat with a constant acceleration of -3.50 m/s$^2$ by reducing the throttle. What is the velocity of the boat when it reaches the buoy?