MAT 225 Game Testing Project Two

Description

The year is 3500 and your spaceship has crashed on the planet Fluxion. Fortunately, your computer has survived the impact,and you open it up to determine the next course of action. You learn that your computer has some maps and information on the civilization, and that the city (and perhaps the planet) was abandoned several years ago. Based on the maps, it appears that your only hope of reaching a communication device is to head to what appears to be the center of a city that you crashed near. Your computer warns you that the city is protected by several gates, which have passcodes to activate. The maps and images show a strange alien language that you have never encountered. You ask your computer if it can translate this language and are told that the language, based on its structure, can only be translated into mathematics. The computer will translate the gates’ riddles and any other information into mathematics. You will need to answer the riddle as posed by your computer (in mathematical language) for it to be able to enter the passcode for the gates. Fortunately, you have a notebook, pencil, and a mathematics text on your computer as supports. You take your supplies, take one last look at your broken ship, and head to towards the first gate. The First Gate Upon arriving at the first gate, you ask your computer to translate the riddle. “These appear to be limits”, your computer replies. “If you provide me with the answer to each of below questions, I will compile, translate, and communicate the passcode to the gate. There is note here that the parameter represents a real number such that .” Your computer also reminds you to type “infinity” for , “-infinity” for , and “NA” if the limit does not exist. You grab your notebook and pencil and begin The Second Gate As you move through the first gate, you can see another gate not far in front of you. You approach the second gate and your computer reads: “There are 2 values for which the below function does not exist. The passcode is the limit of as approaches the smaller of these two values.” Your computer also reminds you to type “infinity” for , “-infinity” for , and “NA” if the limit does not exist. What do you enter for your computer to translate? The Third Gate You arrive at the third gate and look for the inscription. Your computer translates the following: “This passcode consists of the two below limits which include an arbitary real number, . Remember to type “infinity” for ,”-infinity” for , and “NA” if the limit does not exist. Enter the results and I will apply the passcode.” The Fourth Gate You arrive at the fourth gate, feeling confident in your skills. “It is a good thing I had some practice before landing on this planet”, you think. You look carefully at the gate and find the following information, translated by your computer: Each of the limits below represent a piece of the passcode that you must enter to proceed. The parameters and represent positive real numbers and should be treated as such in your answer. “Remember,” says your computer, “to type “infinity” for , “-infinity” for , and “NA” if the limit does not exist.” The Map As you walk through Gate 4, you realize that Gate 5 is nowhere to be found. In front of you lies an expansive desert as far as you can see. You look at your map and see that there is an alert for this area. The warning states that this desert is almost entirely quicksand, with only one path safely through the desert. That path is defined by a piecewise function but requires that some parameters be determined before your computer can generate the plot. Thinking back on what you learned in calculus, you realize that your path will need to be continuous. You just need to tell your computer what the parameters below should be in order to create this continuous path. What parameters do you give your computer? The Fifth Gate After traversing your continuous path, you finally arrive at Gate 5. Your computer reads the gate’s directions to you. “The passcode for this gate is the number found by first entering and then entering using the definitions below. ”What values do you provide to your computer? The Sixth Gate After walking through the fifth gate, your computer informs you that more than half of the gates have been crossed. “Only 4left”, you conclude. “Computer, what is this gate’s riddle?” The Seventh Gate As you approach the seventh gate, you notice that it is only a short distance to the area where your computer indicated the communication device was stored. You look past the gate hopefully, as your computer translates: