MATH 1110 Midterm: MATH 1110 Cornell Exam Exam 3

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turquoisegnu128

31 Jan 2019

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Name: (cid:3) cristina"s section (cid:3) yao"s section: this is a 75-minute exam with 6 problems, put away anything other than pencils, l"h opital"s rule is not allowed, adhere to the honor code. Question 2. (20 points) compute the following limits, if they exist. [you may not use l"h opital"s rule. : lim x 1 log2(x2 + 3) = b) lim x . 2 tan x : lim x sin x + 1 cos x, lim x x x2 + 2x. Question 4. (15 points) this problem is concerned with the function f (x) = xx, for x > 0: explain why the function g(x) = x ln x is continuous. What"s the domain of this function: using part a), deduce that ex ln x is continuous, and show that it is equal to f (x), prove that the equation xx = 3 has a solution.

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please use the following information to answer questions 1-6

Imagine you have graduated and have just gotten a job in a fictionalized version of Paducah, KY, home of the world famous Dippin' Dots (Links to an external site.)Links to an external site.. You got the job by pitching a truly marvelous idea: The Grand Cone-yan, an ice cream festival as grand as any Court Days (Links to an external site.)Links to an external site. or Apple Festival (Links to an external site.)Links to an external site..

The centerpiece of the festival is a 10 foot tall ice cream cone filled with local ice cream dots.

The day before the festival the contractors have brought the truck of ice cream, and begin to fill the cone. After only a single minute, there is a foot of ice cream in your frozen glass cone. Since the entire cone is only 10 feet tall, you decide to come back in 10 minutes to witness the final filling.

You are shocked when you return to find the cone has only been filled to the 2 foot mark! (The worker politely corrects you to say it is actually 2 feet and 2 inches.) You give it another 10 minutes, but the cone is only 2 foot 9 inches filled.

Not knowing what else to do, you make a spreadsheet of the progress.

Time (minutes)	0	1	10	20	30	60	120
Height (feet, inches)	0' 0"	1' 0"	2' 2"	2' 9"	3' 1"	3' 11"	4' 11"

You wonder why they have slowed down so much, so you keep checking in every hour.

Time (hours)	1	2	3	4	5	6
Height (feet, inches)	3' 11"	4' 11"	5' 8"	6' 3"	6' 6"	6' 11"

After six hours you are worried the entire festival might fail, but you won't give up! You keep spreadsheeting.

Time (hours)	7	8	9	10	11	12
Height (feet, inches)	7' 4"	7' 8"	7' 11"	8' 3"	8' 6"	8' 9"

After 12 hours, you take a quick trip home to change clothes, and return to your spreadsheeting.

Time (hours)	13	14	15	16	17	18
Height (feet, inches)	8' 11"	9' 2"	9' 5"	9' 7"	9' 9"	10' 0"

Finally, late in the night, around 3am, it is complete. Your masterpiece. The Grand Cone-yan. But why did it take so long? It took a lot longer than 10 minutes. Why did the workers slow down so much? The first minute finished the first foot, but three feet took 30 minutes instead of 3 minutes. And now it's 3am!

The workers say that they filled at a steady rate of 13 gallons per hour, and that any faster would run the risk of drain freeze.

Your responses

1. What is wrong with the following argument?

If you really did 13 gallons per hour, then the 10 foot cone should have only taken 10 / 13 = 0.7 hours, less than an hour tops.

2. What is wrong the following question?

How do you convert gallons into feet?

3. Find an authoritative source for the volume of a cone. Give the formula and explain what each part of the formula means in this problem.

4. Most formulas will have both radius and height. Find a reasonable source for the relationship between the radius and height of an ice cream cone. Give an expression like

R = H

5. Calculate the volume of the cone using your formula. At a constant rate of 13 gallons per hour, how long should it have taken to fill up?

You may use the approximate formula V=0.02908882 h3 if the formula you discovered does not match at all.

6. There should still be a discrepancy between the V=0.02908882 h3 and the spreadsheet. Can you explain what likely happened?

Given the following main program

#main
a = [5,2,9,6,3] doubleList(a) print a

Implement the function named doubleList that takes one list argument and modifies the list so that each element in the list is doubled. The statement print(a) in the main program will then have to print [10,4,18,12,6]
Given the following main program

#main
a = [5,2,9,6,3]
b = reversedList(a) print b
print a

Implement the function named reversedList that takes one list argument and returns a list that contains the elements in the list argument in reverse order. The statement print(b) in the main program will then have to print [3,6,9,2,5]. The statement print(a) must print the original list [5,2,9,6,3] unaffected. This means your function should not modify the list argument.
Given the following main program

#main
a = [5,2,9,6,3] reverseList(a) print a

Implement the function named reverseList that takes one list argument and reverses the list so that the modified list contains the same elements in reverse order. The statement print(a) in the main program will then have to print [3,6,9,2,5]
What is the return value of the functions doubleList, reversedList and reverseList in questions 1, 2, and 3 above?

Given the following main program

#main
a = [5,2,9,6,3]
b = evenElements(a) print b

Implement the function named evenElements that takes one list argument and returns a list that contains the elements in the list argument that are even integers. The statement print(b) in the main program will then have to print [2,6]. What is the return value of the function? Your function should not modify the list argument.
Given the following main program

#main
a = [5, 2, 9, 6, 3, 7, 19, 4, 8, 17, 21, 20, 15] removeOddElements(a)
print a

Implement the function named removeOddElements that takes one list argument and modifies the list so that all odd integers in the list are removed. The statement print(a) in the main program will then have to print [2,6,4,8,20]. What is the return value of the function?
Part A
#Main program A=[5,8,2,0,-5,3] n=-5
answer = isFound(A, n) if answer == True:

print "The integer is found in the list" else:

print "The integer is not found in the list."

Consider the main program shown above. Write a Python function named isFound that takes a list of integers and an integer as arguments and returns True if the integer is found in the list; otherwise it returns False.

Remark: You are NOT allowed to use the in operator or any other built in function when you write this function. Instead, you must write a loop to go through the elements of the list.

Part B

Give the following main program

#main
A = [5,2,9,6,3]
B = [2,4,3,9,7,1,6,5]
flag = isList1InList2(A, B) if flag:

print "The list", A, "is contained in the list", B else:

print "The list", A, "is not contained in the list", B

Implement the function named isList1InList2 that takes two list arguments and returns True if and only if each element of the first list argument are found in the second list argument; otherwise it returns False.

Remark: You are NOT allowed to use the in operator or any other built in function when you write this function. Instead, if you wish, you can use the function you wrote in Part A.

For the lists shown in the main program, your function must return True because each element of list A is found in list B.

A given List is known as Palindrome List if the reverse of the List contains the same elements in the same order of the original List. For example the List of integers [2, 5, 0, 3, 3, 0, 5, 2] is a Palindrome because the reverse of the List which is [2, 5, 0, 3, 3, 0, 5, 2] contains the same elements in the same order as the given List. However the List [1, 2, '2', 1] is not Palindrome because its reverse which is [1, '2', 2, 1] does not contain the same elements in the same order as the given List.

Write a Python function named isPalindrome that takes a List as argument and returns True if the argument is a Palindrome List; otherwise it returns False. You don't need to write the main program; just write the function. If you would like to test your function, then it is ok to write the main program too but you will not get any mark for the main program.
Given your function in question #7 above, what is the output of the following code: a=[]

b = [5,2,9,6,3]

print isList1InList2(a,b)
Given your function in question #7 above, what is the output of the following code:

a=[]
b=[]
print isList1InList2(a,b)
Given your function in question #7 above, what is the output of the following code: a = [5,2,9,6,3]

b=[]

print isList1InList2(a,b)

Given the following main program

#main
a=[]
n = readListElements(a)
print "The user entered", n, "elements to the list" print a

Implement the function named readListElements that takes one list argument and modifies the list by repeatedly asking the user to enter integer values and then appending them to the list. The process stops when the user enters -1000. The stopping value -1000 should not be appended to the list. Moreover your function must count the appended elements and return it. Example if the user enters the integers 31, -4, 9, 1,-1000 then your function must modify the list a to a = [31, -4, 9, 1] and return the number elements added which is 4.
Write a function named createRandomList that takes an integer argument n and returns a list with n elements. The elements must be random numbers in the range [0,100]

Given the following main program:

#main

   n = int(input("How many elements do you want in your list? "))
   a = createList(n)
   s1 = sumOfElementsAtEvenIndexes(a)
   print s1

   s2 = sumOfElementsAtOddIndexes(a)
   print s2
   s3 = sumOfAllElements1(a)
   print s3

   s4 = sumOfEvenElements(a)
   print s4
   s5 = sumOfOddElements(a)
   print s5

   s6 = sumOfAllElements2(a)
   print s6
   if (s3 != s6):

         print "Something is wrong in your program."
   else:

         print "Looks like you have done a good job."

Implement the functions as follows:

createList: returns a list object with n elements. The elements are generated randomly so that each element is in the range [15,45]
sumOfElementsAtEvenIndexes: returns the sum of the elements at even indexes. Use a for loop or a while loop.
sumOfElementsAtOddIndexes: returns the sum of the elements at odd indexes. Use a for loop or a while loop.
sumOfAllElements_A: returns the sum of all the elements in the list using the functionssumOfElementsAtEvenIndexes and sumOfElementsAtOddIndexes. Here you are NOT allowed to use any loop; instead make function calls as described.
sumOfEvenElements: returns the sum of the even integer elements in the list. Use a for loop or a while loop.
sumOfOddElements: returns the sum of the odd integer elements in the list. Use a for loop or a while loop.
sumOfAllElementsB: returns the sum of all the elements in the list using the functions sumOfEvenElements and sumOfOddElements. Here you are NOT allowed to use any loop; instead make function calls as described.

17. Most data compression algorithms like winzip, gzip, lzip and etc are based on the frequency distribution of characters in a given string. Write a function named getFreqDistribution that takes a string argument and returns a LIST that has length 26 such that the first element of the list is the number of appearance of 'a' or 'A' in the string, the second element is number of appearance of 'b' or 'B', and so on so forth.

I'm studying python 2 and have a lot of troubles with solving these homework questions.

grayelk171

MATH 1110 Midterm: MATH 1110 Cornell Exam Exam 3

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