Work the problems below as directed. Show all work. Clearly mark your final answers. Use exact values unless the problem specifically directs you to round. Simplify as much as possible. Partial credit is possible, but solutions without work will not receive full credit. Part 1: These questions you will submit answers to in Canvas. Show all work and submit the work with Part 2 of the exam. But you must submit the answers in Canvas to receive credit. Each question/answer will be listed separately. The Canvas question will refer to the number/part to indicate where you should submit which answer. The questions will appear in order (in case there is an inadverten t typo). Correct answers will receive full credit with or without work in this section, but if you don’t submit work and clearly label your answers, you won’t be able to challenge any scoring decisions for making an error of any kind. 1. Find the limit of th e infinite series. (10 points) 2. Determine the convergence or divergence of each series. (6 points each) a. b. ∑ 1 (− 1)4/5 ∞ = 2 c. d. ( ) = + 1 2 4 n n n = − 1n n ne = − 1 3 1 4 1 n n = + − − 1 2 5 2 3 5 n n n n e. f. g. 3. For the series , if the series converges, does it converge conditionally or absolutely? Find the partial sum of the first six terms and then state the maximum error on the sum at that term. (16 points) 4. Find N such that for the convergent series. (10 points) 5. Use the first four terms of the Taylor series to approximate . (10 points) ( ) = + − 1 1 ln )1 ( n n n = + − 1 2 1 3 2 )1 ( n n n n n n n n 2 1 1 3 2 = + − 1 2 1 ( 1) n n n + = − 0.001 NR 4 1 1 n n = − 1 0 2dx e x 6. For the sequence below. i) Determine if the sequence is monotonic (or is monotonic after some finite value of n). You may determine this graphically or by calculating derivatives. ii) Determine the bounds (above and below of the sequence). iii) Can you apply the bounded & monotonic theorem for convergence to this sequence? iv) Does this sequence converge by another theorem? If so, which one? v) If the sequence converges, what does it converge to? ( 20 points) Part 2: In this section you will record your answers on paper along with your work. After scanning, submit them to a Canvas dropbox as directed. Th ese questions will be graded by hand. 7. Find an expression for the nth partial sum of . (12 points) 8. For each of the series in #2, state the test used to determine convergence. (9 points each) a. b. ∑ 1 (−1)4/5 ∞ =2 c. /2n na ne − = ( ) = + 1 2 4 n n n = − 1n n ne = − 1 3 1 4 1 n n d. e. f. g. 9. Determine the radius of convergence for the series . State the interval of convergence and clearly indicate whether it is open, closed or half -open. (10 points) = + − − 1 2 5 2 3 5 n n n n ( ) = + − 1 1 ln )1 ( n n n = + − 1 2 1 3 2 )1 ( n n n n n n n n 2 1 1 3 2 = + − = + + − 0 1 )1 ( )1 ( n n n x n 10. Find the nth Taylor polynomial centered at the given c. Use the included table to show work.
(15 points) n n! 0 1 2 3 4 5 6 11. Find a power series for the functions using the geometric series method. (20 points each) a. b. ( ) cos 4 , 6, 2 g x x n c = = = () ()nfx () ()nfc () n xc− () () () !
n n fc xc n − ()nPx = 3 () 21 fx x = − 3 24 7 () (1 3 ) x fx x = +
Ms. F, 48 years old, has been admitted to the hospital with severe abdominal pain. Earlier that day she had generalized abdominal pain, followed by a severe pain in the lower right quadrant of her abdomen, accompanied by nausea and vomiting. That evening she was feeling slightly improved and the pain seemed to subside somewhat. Later that night, severe, steady abdominal pain developed, with vomiting. A friend took her to the hospital, where examination demonstrated lower right quadrant tenderness and mild abdominal rigidity. Fever and leukocytosis indicated infection. A diagnosis of acute appendicitis, with possible perforation, was indicated, with immediate surgery.
Discussion Questions
Why is the sequence of pain (location and type of pain) significant in the diagnosis of acute appendicitis? Describe the rational for each type of pain. Does this sequence confirm the diagnosis?
Using the pathophysiology, describe the reason for:
the pain subsiding and then recurring.
leukocytosis and fever.
abdominal rigidity.
Ms. T, age 28 years, has noticed urgency, frequency, and dysuria recently, as well as an unusual odor to the urine. Urinalysis indicated a heavy concentration of Escherichia coli in the urine, some pus, and WBCs. Ms. T was prescribed antibiotics, which she took for the first few days. This seemed to give her relief, but she then stopped taking the medication. Within a few days, the symptoms returned, but she decided to “just live with it.”
Discussion Questions
Explain why women are predisposed to cystitis.
What preventive measures are important in reducing recurrence?
Discuss other signs and symptoms that may indicate cystitis.
What potential problems may she experience if she does not adhere to the treatment prescribed?
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Premium papers. We provide the highest quality papers in the writing industry. Our company only employs specialized professional writers who take pride in satisfying the needs of our huge client base by offering them premium writing services Why is the sequence of pain (location and type of pain) significant in the diagnosis of acute appendicitis? Describe the rational for each type of pain.
Assessment Type Individual – Application Code Length or Duration Four (4) Programs / Tasks Subject Learning Outcomes SLO 2, SLO 3, SLO 4 Weighting 25% Assessment Purpose Many common problems solved by programmers include manipulation of numeric values and lists of numbers. In this assessment, you will use your understanding of the fundamental programming principles to solve four problems that involve numbers. Assessment Item For this assessment, you must submit four (4) algorithm descriptions and C++ programs, one for each task described in the brief below Assessment Instructions This assessment consists of four (4) tasks. You will need to prepare the following two components for each task. Component 1: Algorithms An algorithm is a set of well-defined instructions in sequence to solve the problem. An algorithm should not be computer code. Instead, the algorithm should be written in such a way that it can be used in similar programming languages to implement a solution in code. Example: Find the largest of two numbers entered by the user. Step 1: Start Step 2: Declare variables a and b Step 3: Get input from the user for a and b Step 4: if a is greater than b Step 4.1: print a Step 5: if b is greater than a Step 5.1: print b Step 6: Stop Component 2: C++ Coding You will provide a C++ program for each of the four (4) questions given below that implements the algorithm you describe in Part 1. CRICOS: 02155J / HE PROVIDER: Assessment Tasks Task 1 – Grading System Write a program that allows the user to enter the mark scored within a range of 0 – 50. Given a positive value, do the following: ? If the given score is between 0 and 50 (0 = score = 50), then calculate the percentage (e.g., 100% for 50, 75% for 37.5, etc…). A percentage is a number or ratio that represents a fraction of 100. ? Calculate the grade from the percentage received. The grade will be: F, if the percentage is 0 – 59.99. D, if the percentage is 60 – 69.99. C, if the percentage is 70 – 79.99. B, if the percentage is 80 – 89.99. A, if the percentage is 90 – 100. ? If the given score is greater than 50, print “Score is greater than 50.”. Example 1 Please enter your score: 32.6 You have passed with 65.2%, and received a grade D. Example 2 Please enter your score: 10.5 You have failed with 21%, and received a grade F. Example 3 Please enter your score: 50 You have passed with 100%, and received a grade A. Example 4 Please enter your score: 74 Score is greater than 50. Note: Inputs from the user are shown in bold blue. Task 2 – Calculate Miles per Gallon Write a program that allows a user to enter the litres of petrol consumed and the number of miles travelled by the car. Given a positive value for both litres of petrol and miles travelled, calculate the number of miles per gallon the car delivered. One litre of petrol is 0.264179 gallons. You must show the output in three decimal places as shown in the example. Example Please enter the number of litres of petrol consumed: 15.5 Please enter the number of miles travelled: 75 Petrol Consumed: 15.500 Miles Travelled: 75.000 Miles per gallon: 18.316 Note: Inputs entered by the user are shown in bold blue. Task 3 – Looping Through all Numbers from Start to Finish Write a program that prompts the user to input two (2) integer values; a starting value and an end value. Loop through all the values from start to end, which should include the start and end values. For each value: ? If the number is divisible by both 3 and 5, print the word “ticktock”. For example for 15, 30, and 45 you would print “ticktock”. ? Else if it is a multiple of 3 (value % 3 == 0), print the word “tick”. For example, for 3, 6, and 9 you would print “tick”. ? Else if it is a multiple of 5 (value % 5 == 0) , then print “tock ”. For example, for 5, 10, and 20 you would print “tock”. ? Else if it is not divisible by 3 or 5, print the number. For example, for 1 you would just print ‘1’. Example Please enter a start value: 4 Please enter an end value: 15 tock tick 7 8 tick tock 11 tick 13 14 ticktock Note: Inputs entered by the user are shown in bold blue. Task 4 – Order Numbers Write a program that prompts the user to input 3 integer values and print these values in ascending and descending order. Example Please enter the first number: 45 Please enter the second number: 12 Please enter the third number: 78 Ascending order: 12 45 78 Descending order: 78 45 12 Note: Inputs entered by the user are shown in bold blue. Submission All work must be submitted via the LMS, in the assignments section appropriate to this brief. Please ensure the above mentioned submission date and/or time are adhered to, or penalties may apply. You should submit a compressed (zip) file containing your C++ solutions folder. Within this file, each task must have its own file. Please ensure you use the following naming conventions for this submission. Your zip file should be named using the following convention: [Student_ID][Surname][First Name][SubjectCode][Assessment_#] E.g.: 1234_Singh_Visha_PRG1002_Assessment_02 Each task within the zip file should follow this convention: [Task_#][Student_ID] [SubjectCode][Assessment#] E.g.: Task_1_1234_PRG1002_Assessment_02 Therefore, your zip file should consist of four (4) individual files, that each use the above mentioned naming format. For more information on late submission, please see the Assessment Policy. Academic Integrity The integrity of the assessment process is fundamental for ensuring appropriate evaluation at AIT. All work submitted should be your own, and where additional resources are used, they must be referenced according to the Harvard style. Additionally, Turnitin is available in the LMS to test plagiarism in your writing. For more information on academic integrity, please see the Academic Integrity and Academic Integrity Penalties Policies. Appeals Fair application of the assessment rubric, rules and guidelines should be administered for each assessment. If you feel an evaluation requires further consideration, you may be entitled to an appeal. For more information on your right to an appeal, please see the Assessment Appeals Procedure and Policy. Policies For access to the policies mentioned above and related to education at AIT, please see the footer of the AIT website, and follow the link named Education Policies and Procedures. Website: https://www.ait.edu.au Assessment Rubric Task Descriptor (F) Fail (P) Pass (C) Credit (D) Distinction (HD) High Distinction Ability to produce appropriate readable comments in code 15% No comments Major lack of comments make it difficult to understand the code A few lines of code are commented on, but do not adequately explain what the code intends to accomplish Important lines of code are commented on and are useful in understanding what the code accomplishes, or the code is overly commented on Comments are succinct, well-written and clearly explain what the code intends to accomplish Produces organised code with adequate indentation and correct naming conventions 10% No clear organisation in code Some organisation, indentation and use of correct naming conventions with some exceptions Organisation, indention, and use of naming conventions produces readable code with few exceptions Organisation, indention, and use of naming conventions produces readable code without exception Organisation, indention, and use of naming conventions produces readable code without exception and follows documented best practices supported by correctly cited resources Ability to apply appropriate variables or data structures (i.e., array) 15% Not able to identify required data type or data structure Able to identify required data type or data structure but they are not applied correctly and correct results are not produced Able to identify and apply required data type or data structure, and they are applied adequately, although correct results are not produced Able to identify and apply required data type or data structure and produce partially correct results Able to identify and apply required data type or data structure and produce correct results Ability to analyse problems and identify appropriate requirements 20% Unable to identify any input and output based on stated problems Able to identify only one input and output based on stated problems Able to identify correct inputs and outputs based on stated problems with some errors or missed cases for one problem Able to identify solutions, inputs and outputs for all stated problems Able to identify correct solutions, inputs and outputs for all stated problems including corner cases Ability to identify and apply correct control structures (sequential, selective, and loops) 30% Not able to identify required control structures Able to identity required control structures but does not apply them correctly Able to identify and apply required control structures but with limited evidence of correct results Able to identify and apply required control structures and produce correct results with few exceptions Able to identify and apply required control structures and produce correct results without exception Ability to keep the program free from syntax, logical and run-time errors 10% Unable to run the program due to syntax or runtime errors Able to create a program but with logic errors Able to create a program that runs without any logic errors Able to create a program that runs without any logical errors but that does not produce correct output Able to create a program that runs without any logical error and displays appropriate outputs CRICOS: 02155J / HE PROVIDER:
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Assessment 2: Applying the TLL model to a sequence of teaching (60%) Word Count: 3000 words. In your role as a teacher, and drawing from the weekly content in this subject, apply and analyse the three layers in our TLL model (Neuroscience, Psychology, Educati^to the planning of a sequence of teaching in your practice. A sequence of teaching is a block of content you plan to teach (or have taught or a hypothetical teaching session) and should include at least 3 hours of content, activities and assessment task/s. You will consider the TLL Model against each of these areas. Your submission will include the following: • A description of the sequence of teaching • Outline how each TLL layer is applied to the sequence of teaching • Discuss the challenges and strengths in applying each layer of the model to the sequence of teaching • Discuss the benefits to your teaching in applying the model • Discuss and reflect on the potential benefits to student learning in applying the model • Draw conclusions using a summative statement about the worth of applying the model to teaching in the classroom and / or teaching and / or learning context appropriate to your area of interest. If you are not a teacher / actively teaching in the classroom: • Try to choose a context for teaching and learning that is relevant to your area of interest and professional context • If you are not actively engaged in the workforce, you are welcome to use a hypothetical situation where teaching and learning are the central goals • The main thing is to adapt the lessons and insights you have gained over the previous weeks to better inform your teaching and learning practice (in whatever context you decide). The broad purpose of this assessment is for you to apply your learning from this subject to your teaching and reflect on its utility. More specifically the task requires you to engage and draw from the weekly content and relevant literature and apply this to a teaching sequence in the classroom or another context relevant to you. For example, think about how your knowledge of brain structures may help in understanding how learning may occur and how that might influence your approaches to teaching within the sequence? What evidence is there in the research literature to support your ideas?
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