[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-451103-105":59,"doc-detail-451103-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","calculus-i-un1101-practice-final-a","Calculus I (UN1101) Practice Final A","","Calculus I practice final A for a 150-minute exam with 10 pages and 6 questions, totaling 80 points. The instructions require clear, legible work and prohibit calculators, computational devices, and consulting others, while allowing notes and the textbook. Topics assessed include discontinuity analysis with asymptotes, limits, Mean Value Theorem applications, derivatives and extremum/inflection identification, logistic modeling with linearization and approximation, and Riemann sums and exact area computation.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/calculus-i-un1101-practice-final-a/451103/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/calculus-i-un1101-practice-final-a/451103.png","ImageObject",300,407,{"name":92,"@type":93},"Mia  ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-21","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How long is the Calculus I practice final A and how many points are possible?","Question",{"text":113,"@type":114},"The exam allows 150 minutes and contains 6 questions with a total of 80 possible points.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Are calculators or computational devices allowed during the exam?",{"text":118,"@type":114},"No. Calculators, computational devices, and consulting other people are not allowed during the exam duration.",{"name":120,"@type":111,"acceptedAnswer":121},"What topics are covered across the six questions?",{"text":122,"@type":114},"The questions cover discontinuities and asymptotes, evaluating limits, derivatives with extrema and inflection points, linearization for a logistic model, and Riemann sums and exact area under a curve.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},451103,1790884619,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145},687207024478,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Calculus I (UN1101) Practice Final A Instructor: Robin Zhang  \nStudent Name (UNI) :    \nInstructions:  \nThis exam contains 10 pages (including this cover page) and 6 questions. The total number of possible points is 80 points. You will have 150 minutes to complete this exam.  \n􀀏 Print your name and UNI in the space above.  \n􀀏 Answer the questions in the space provided on the question sheets. You may use extra paper.  \n􀀏 Clearly identify and simplify your answers. You will not receive full credit if there are multiple apparent answers, even if one of them is correct.  \n􀀏 Write legibly and show your work. You may receive partial credit for intermediate steps. Correct answers without any reasoning or work will not receive full credit.  \n􀀏 No calculators, computational devices, or consulting other people during the duration of this exam. Any cheating will result in an automatic failing grade in the course and potential administrative action.  \n􀀏 You may consult your notes and textbook for this exam. This does not include WebAssign, Courseworks, or other online resources.  \n􀀏 Upload your exam to Gradescope via PDF or images at the end of the time allotted. At the end of the exam, you have 15 minutes to upload your exam. Any exams uploaded after the end of the upload period will not be accepted.  \n􀀏 Remain in the Zoom call with your camera. If you need to leave your work area for any reason, please inform the instructor beforehand.  \nDo not write in the table to the right.  \n\n| Question | Points | Score |\n| --- | --- | --- |\n| 1 | 12 |  |\n| 2 | 16 |  |\n| 3 | 21 |  |\n| 4 | 9 |  |\n| 5 | 16 |  |\n| 6 | 6 |  |\n| Total: | 80 |  |\n\n1. Consider the function  \nf (x) = (six(x􀀙)  \nif x > 􀀙  \nif x 􀀔 􀀙  \n(a) (4 points) Identify the real numbers at which f (x) is discontinuous.  \nHint: You should justify why f(x) is discontinuous at certain values of x and why f(x) is continuous everywhere else.  \n(b) (4 points) Identify the horizontal and vertical asymptotes of f (x) .  \n(c) (4 points) What does the Mean Value Theorem say about f (x) on the interval [2􀀙; 3􀀙]?  \n2. Find the limit if it exists. If the limit does not exist, explain why.  \n(a) (4 points)  \nx2 + 1 lim ~~  ~~x! 1 x 􀀀 1  \n(b) (4 points)  \ne 􀀀x lim ~~  ~~x!1 ex + 1  \n(c) (4 points)  \n2x2 􀀀 2 lim ~~  ~~x!1 􀀀2x + sin(x)  \n(d) (4 points)  \nlxi0 x2 cos 􀀒 1x􀀓  \n3. Consider the function  \nf (x) = 2x3 + 9x2 + 12x + 1 :  \n(a) (3 points) State the domain and range of the function f (x) .  \n(b) (4 points) Find f 0 (x) and f 00 (x) .  \n(c) (5 points) Find the local extrema of f (x) .  \n(d) (4 points) Find all of the values of x where f (x) has an in􀀍ection point.  \n(e) (5 points) Sketch a graph of y = f (x) and label its extrema, in􀀍ection points, and asymptotes.  \n4. The spread of a rumor over time within a town with a population of 12000 people can be modeled by a logistic function  \n 12000  R (t) = 1 + e 􀀀t :  \nThe logistic function R (t) gives the number of people at time t who have heard the rumor.  \n(a) (6 points) Find the linearization of R (t) at t = 0 .  \n(b) (3 points) Use linear approximation at t = 0 to estimate the number of people in the town who have heard the rumor at time t = 1 .  \n5. Consider the curve y = x3 + x.  \n(a) (5 points) Approximate the area under the curve between x = 0 and x = 4 by a Riemann sum of four rectangles using right endpoints.  \n(b) (4 points) Express the area under the curve as the limit of a Riemann sum.  \nYou do not need to evaluate the area for this part. You can leave your answer as a limit.  \n(c) (5 points) Find the exact area under the curve between x = 0 and x = 4 .  \nHint: you do not have to use the limit from part (b); you 􀀌nd the area using any method covered in class.  \n(d) (2 points) Is the Riemann sum approximation of the area under the curve from part (a) an overestimate, an underestimate, or neither?  \n6. (6 points) Evaluate  \nZ ~~ ~~cos22(t) s6 + sincos((tt)) + t! dt:","cbCaisJyAsQpZwbC","https://ap.wps.com/l/cbCaisJyAsQpZwbC","pdf",137236,"English","# Exam Instructions\n# Question 1\n# Question 2\n# Question 3\n# Question 4\n# Question 5\n# Question 6","[{\"question\":\"How long is the Calculus I practice final A and how many points are possible?\",\"answer\":\"The exam allows 150 minutes and contains 6 questions with a total of 80 possible points.\"},{\"question\":\"Are calculators or computational devices allowed during the exam?\",\"answer\":\"No. Calculators, computational devices, and consulting other people are not allowed during the exam duration.\"},{\"question\":\"What topics are covered across the six questions?\",\"answer\":\"The questions cover discontinuities and asymptotes, evaluating limits, derivatives with extrema and inflection points, linearization for a logistic model, and Riemann sums and exact area under a curve.\"}]","Calculus I (UN1101) Practice Final A | PDF",1790734385,25]