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Pennsylvania State University Penn State Main Campus Calculus Questionnaire

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5/8/2020 Quiz: Final Exam (140S20) Final Exam (140S20) Started: May 8 at 12:58pm Quiz Instructions UNLESS SPECIFICALLY NOTED ON A PROBLEM, YOU WILL NEED TO SHOW WORK TO RECEIVE FULL CREDIT. You will need to upload your work in a SINGLE file. There are only seven questions where no work is required (problems 17-23). For the other 16 questions the work is worth 3 points per problem, for a total of 48 points. Before you start this, make sure you practice uploading your work. The recommended setup is to use the CamScanner app on your phone/tablet to merge your work photos into a single .pdf file. You will not be able to upload more than one file, so it is extremely important you find a way that works for you to create a single file with your work BEFORE you start this exam. ONCE YOU BEGIN THERE IS A 140 MINUTE TIME LIMIT. IF YOU DO NOT UPLOAD YOUR WORK FILE IN THIS QUIZ YOU MUST EMAIL IT TO YOUR PROFESSOR IMMEDIATELY. WORK SUBMITTED OUTSIDE THE QUIZ MAY BE SUBJECT TO A 5% PENALTY. While you are taking the exam, you will be expected to work entirely on your own. You are required to maintain academic integrity during the exam to provide a fair testing environment for yourself and other students in the course. Question 1 Evaluate 3 pts . -1/4 1 0 https://psu.instructure.com/courses/2051605/quizzes/3884620/take 1/18 5/8/2020 Quiz: Final Exam (140S20) Question 2 Evaluate 3 pts . 1 -1 0 Question 3 Suppose that 3 pts . Find . 2 3 5 0 The limit does not exist. Question 4 3 pts Consider the graph of the function f(x) given below. https://psu.instructure.com/courses/2051605/quizzes/3884620/take 2/18 5/8/2020 Quiz: Final Exam (140S20) Let . Calculate . -8 16 8 -16 -2 Question 5 Let and 3 pts Suppose https://psu.instructure.com/courses/2051605/quizzes/3884620/take . Calculate 3/18 5/8/2020 Quiz: Final Exam (140S20) Question 6 3 pts A 13 ft long ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 2 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 5 ft from the wall? ft/s ft/s ft/s ft/s ft/s Question 7 Find the linearization of the function 3 pts at and use it to approximate the value of f(6). 25 33 29 8 https://psu.instructure.com/courses/2051605/quizzes/3884620/take 4/18 5/8/2020 Quiz: Final Exam (140S20) 4 Question 8 3 pts Find the absolute maximum value M and the absolute minimum value m of the function on the domain [1,9]. M = [ Select ] m = [ Select ] Question 9 3 pts Suppose that the SECOND DERIVATIVE of a function is given by . Find the x-coordinates of inflection points of the curve . 0 and 4 only 2 and 4 only 0 only 0, 2, and 4 0 and 2 only Question 10 https://psu.instructure.com/courses/2051605/quizzes/3884620/take 3 pts 5/18 5/8/2020 Quiz: Final Exam (140S20) Suppose that the FIRST DERIVATIVE of a function is given by . Find the critical numbers of and determine whether a local maximum, a local minimum, or neither occurs at each. local min at -5, local max at 0, local min at 3 local min at -5, local max at 0, neither max nor min at 3 local max at 0, local min at -5, no other critical numbers local max at -5, local min at 0, neither max nor min at 3 local max at -5, local min at 0, local max at 3 Question 11 3 pts You are building an open-top aquarium with a square base with side length x ft. Material for the base costs $30 per square foot, while glass for the sides costs $10 per square foot. The volume of the aquarium needs to be 400 cubic feet. To find the dimensions of the cheapest suitable aquarium, which function should you minimize? Question 12 https://psu.instructure.com/courses/2051605/quizzes/3884620/take 3 pts 6/18 5/8/2020 Quiz: Final Exam (140S20) Find two nonnegative numbers such that the sum of first number and 3 times the second number is 1200 and the product of the numbers is as large as possible. For full credit, you MUST justify that your answer gives the absolute maximum. first number is 900 first number is 600 first number is 500 first number is 200 first number is 300 Question 13 3 pts A particle moves in a straight line with acceleration , initial velocity v(0) = 2 and initial position s(0) = 5. Find the position function. . Question 14 https://psu.instructure.com/courses/2051605/quizzes/3884620/take 3 pts 7/18 5/8/2020 Quiz: Final Exam (140S20) Find for . Recall is the Riemann sum with 3 equal length subdivisions using LEFT ENDPOINTS as sample points. 96 46 120 23 78 Question 15 Let 3 pts . Calculate Question 16 Evaluate https://psu.instructure.com/courses/2051605/quizzes/3884620/take . 3 pts . 8/18 5/8/2020 Quiz: Final Exam (140S20) Question 17 Consider 6 pts . Is f(x) differentiable at x=0? [ Select ] Is f(x) continuous at x=0? [ Select ] Consider . Is g(x) differentiable at x=0? [ Select ] Is g(x) continuous at x=0? [ Select ] YOU DO NOT NEED TO SHOW WORK FOR THIS PROBLEM. Question 18 https://psu.instructure.com/courses/2051605/quizzes/3884620/take 6 pts 9/18 5/8/2020 Quiz: Final Exam (140S20) Suppose that f is a function such that Then and that is [ Select ] . , and is [ Select ] . The choices for both dropdown are A) B) 0 C) D) E) YOU DO NOT NEED TO SHOW WORK FOR THIS QUESTION. Question 19 6 pts Find all asymptotes of the graph of the function . Horizontal asymptote(s) are [ Select ] asymptote(s) are [ Select ] , and vertical . YOU DO NOT NEED TO SHOW WORK FOR THIS QUESTION. https://psu.instructure.com/courses/2051605/quizzes/3884620/take 10/18 5/8/2020 Quiz: Final Exam (140S20) Question 20 6 pts Select the graph of a function f that satisfies and . YOU DO NOT NEED TO SHOW WORK FOR THIS QUESTION. https://psu.instructure.com/courses/2051605/quizzes/3884620/take 11/18 5/8/2020 https://psu.instructure.com/courses/2051605/quizzes/3884620/take Quiz: Final Exam (140S20) 12/18 5/8/2020 https://psu.instructure.com/courses/2051605/quizzes/3884620/take Quiz: Final Exam (140S20) 13/18 5/8/2020 https://psu.instructure.com/courses/2051605/quizzes/3884620/take Quiz: Final Exam (140S20) 14/18 5/8/2020 Quiz: Final Exam (140S20) Question 21 Write 6 pts as the limit of Riemann sums with equal length subintervals using RIGHT ENDPOINTS as sample points. YOU DO NOT NEED TO SHOW WORK FOR THIS PROBLEM. https://psu.instructure.com/courses/2051605/quizzes/3884620/take 15/18 5/8/2020 Quiz: Final Exam (140S20) Question 22 Suppose that 6 pts . Calculate . YOU DO NOT NEED TO SHOW WORK FOR THIS QUESTION. 14 30 18 28 50 Question 23 18 pts Suppose that f is invertible, f'(x) is continuous, and that f and f’ satisfy the following.
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