Find the maximum and minimum points on the graph of $x^{2}+4 y^{2}-2 x-16 y+13=0$, (a) without using calculus. (b) using calculus.

(a.) State the first fundamental theorem of calculus. (b.) State the second fundamental theorem of calculus.

What is the value of the engineering software packages in (a) engineering education and (b) engineering practice?

What is the Urinary System?

Identify the organs of the urinary system.

On page 431 of Physics: Calculus, $2 d$ ed., by Eugene Hecht (Pacific Grove, CA: Brooks/Cole, 2000), in the course of deriving the formula $T=2 \pi \sqrt{L / g}$ for the period of a pendulum of length $L$, the author obtains the equation $a_T=-g \sin \theta$ for the tangential acceleration of the bob of the pendulum. He then says, "for small angles, the value of $\theta$ in radians is very nearly the value of $\sin \theta$; they differ by less than $2 \%$ out to about $20^{\circ} . "$

Use a graphing device to determine the values of $x$ for which $\sin x$ and $x$ differ by less than $2 \%$. Then verify Hecht's statement by converting from radians to degrees.

All 80 rooms in a motel will be rented each night if the manager charges $\$40$ or less per room. If he charges $\$(40+x)$ per room, then 2x rooms will remain vacant. If each rented room costs the manager $\$10$ per day and each unrented room $\$2$ per day in overhead, how much should the manager charge per room to maximize his daily profit?

The total cost C of ordering and storing x units is $C=2 x+(300,000 / x)$. What order size will produce a minimum cost?

The Springfork Amateur Golf Club has a tournament every weekend. The club president has asked you to write two programs:

1. A program that will read each player’s name and golf score as keyboard input, and then save these as records in a file named golf.txt. (Each record will have a field for the player’s name and a field for the player’s score.)
2. A program that reads the records from the golf.txt file and displays them.

Analyze the graph of the function. Label any extrema and/or asymptotes that exist. f(x) = x-2 / x²-4x+3

Determine whether the statement is true or false. If it is false, explain why. Statement: Prove that if f′(x) = 0 for all x in an interval (a, b), then f is constant on (a, b).

Create a function whose graph has the indicated characteristics. (The answer is not unique.)
Vertical asymptote: $x=5$ Horizontal asymptote: $y=0$

Assume that a file containing a series of integers is named numbers.txt and exists on the computer’s disk. Write a program that displays all of the numbers in the file.

A high-speed lifting mechanism supports an 800-kg object with a steel cable that is 25.0 m long and 4.00 cm$^2$ in cross-sectional area. By what additional amount does the cable increase in length if the object is accelerated upward at a rate of 3.0 m/s$^2$?