[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-462556-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-462556-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","ap-calculus-ab-chapter-one-test","AP Calculus AB - Chapter One Test","","Practice and test questions for AP Calculus AB, focused on limits, continuity, vertical asymptotes, and numerical approximation. Includes True/False statements about limit behavior, problems asking for indeterminate forms, evaluating limits of trigonometric and algebraic expressions, and interpreting limit and continuity from a given graph. Also contains advanced-style AP TEST QUESTION sections covering AP test logic, including existence of solutions, vertical asymptote detection, and function construction with specified discontinuities.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/ap-calculus-ab-chapter-one-test/462556/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/ap-calculus-ab-chapter-one-test/462556.png","ImageObject",300,407,{"name":42,"@type":43},"Olivia Brown","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-02","2026-09-30",true,{"@type":52,"interactionType":53,"userInteractionCount":26},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"How do you handle a limit when the function is undefined at the point?","Question",{"text":62,"@type":63},"If f is undefined at x=c, the limit can still exist. The worksheet’s True/False item tests that the limit does not automatically fail just because f(c) is undefined.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What does it mean for a discontinuity to be removable vs non-removable?",{"text":67,"@type":63},"A removable discontinuity occurs when the function can be redefined at the point to match the limiting value. A non-removable discontinuity occurs when left/right behavior does not match or the limit does not settle to a single finite value.",{"name":69,"@type":60,"acceptedAnswer":70},"How do you find vertical asymptotes from an expression for f(x)?",{"text":71,"@type":63},"Vertical asymptotes occur where the denominator goes to zero (and the function does not simplify to a finite value). The worksheet includes a multiple-choice problem asking which x-values produce vertical asymptotes.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},462556,1790764484,{"code":4,"msg":81,"data":82},"success",[83,87,91,94,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":92,"slug":93},70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":95,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":26,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":95,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":79,"read_time":143,"preview_page_count":4},16904993612988,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Name:    \nSHOW YOUR WORK FOR CREDIT! No Calculators  \n1) lim -x2 + 4xx → 2  \na) 0 b) 12 c) 4 d) -12 e) None of these  \n~~ ~~ 5x +10  \n2) lim ~~  ~~x→3 x-3  \na) indeterminate b) does not exist c) 25 d) 1 e) None of these  \n x   \n3) lim  \nx→0 tanx  \n4) lim 1 +  1  \nx→0 − x  \na) 1 b) - ∞ ∴does not exist c) ∞ ∴does not exist d) 1 e) None of these  \n5) lim sin􀁓x  \nx →1  \n6) True or False: If f is undefined at x = c, then the limit of f(x) as x approaches c does not exist.  \n7) True of False: If the lim f (x) = L then f(c) = L.  \nx→c  \n􀂭􀂰 x 2 − 3x + 6 when x 􀀟 2  \n8) lix f(x) when f(x) = 􀂮􀂯􀂰− x2 + 3x + 2 when x 􀁴 2  \n9) Find a c such that f(x) is continuous on the entire real line.􀂭􀂰x2 when x 􀁤 4  \nf(x) = 􀂮 c  \n􀂰􀂯  x when x 􀀡 4  \nUse the graph at the right to answer questions 10 – 13.  \n10) lim f(x) = x→2  \n11) lim f(x) = x→4+  \n12) lim f(x) = x→4--  \n13) l im f(x) = x→0  \n\n|  |  | 6 | |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  | f |  |  |  |\n|  |  | 4 |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | 2 |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | 5 |  |  |  |  | 1 | 0 |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | -2 |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  | -4 |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n14) Find the x-values (if any) at which fis discontinuous. Label as removable or non-removable.  \n 2x + 6   \nf(x) = 2  \n2x −18  \na) x = 3 only….Non-removable  \nb) x = -3 only…Non-removable  \nc) x = 3 and x = -3…Both non-removable  \nd) x = -3…Removable, x = 3…Non-removable  \ne) There are no discontinuities  \n15) Determine all of the vertical asymptotes of f(x):  \n x + 2   \nf(x) = 2  \nx -4  \na) V.A at x = 2 only b) V.A. at x = -2 only c) V.A. at x = -2 and x = 2 d) No V.A’s e) None of these  \nx 2-a2  \n16) AP TEST QUESTION: If a 􀁺 0, then lim ~~ ~~ is:  \nx→−a x 4-a4  \n 1   1   1   \na) 6a2 b) 0 c) a2 d) 2a2 e) Does not exist  \n17) AP TEST QUESTION: If the function fis continuous on the closed interval [0, 2] and has values that are given in the table below, then the equation f(x) = ½ must have at least TWO solutions in the interval [0, 2] if k = ? Hint! Draw a picture!  \n\n| x | 0 | 1 | 2 |\n| --- | --- | --- | --- |\n| f(x) | 1 | k | 2 |\n\na) 0  \nb) ½  \nc) 1  \nd) 2  \ne) 3  \n18) AP TEST QUESTION: The graph of the function fis shown to the right.  \nWhich of the following statements is false?  \na) x = a is in the domain of f.  \nb) l im f(x) is equal to l im f(x) x→a+ x→a −  \nc) lim f(x) exists x→a  \nd) lim is not equal to f(a) x→a  \ne) fis continuous at x = a  \nAP Calculus AB Name:  \n_________________________________  \nChapter One Test Period:  \n____  \nSHOW YOUR WORK FOR CREDIT! Calculators are okay!  \n1) Mr. Cook drops his calculus book off of the top of a 220-meter building.  \na) Write a position function.  \nb) When will the book hit the ground? (Round to three decimal places)  \nc) Using the velocity function below, find the velocity of the book when t = 2.  \ns(a)-s(t)  \nVelocity function: lim  \nt→a a-t  \n2) Approximate the limit numerically by completing the table:  \nx 2  \nlim ~~ ~~ = ___________  \nx→−2 x-2  \n\n| x | 1.9 | 1.99 | 1.999 | 2 | 2.001 | 2.01 | 2.1 |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| f(x) |  |  |  |  |  |  |  |\n\n3) Find a function f(x) such that f(x) has a gap at x = 7 and a vertical asymptote at x = -4.  \n4) On the graph to the right, draw a function that has the following properties:  \n• A step (or jump) discontinuity at x = 5  \n• f(5) = 6.  \n(x + 􀀧x)2 − 2(x + 􀀧x)+ 1− (x2 − 2x + 1)  \n5) Find the limit: lim ~~ ~~  \n􀀧x→0 􀀧x  \n6) Find the limit: lim cos  1  \nx→0 x  \n7) On the graph below, draw the function y = 4 – x2 in the first quadrant. Then draw four circumscribed rectangles of equal ","cbCaihI2TYlTxItO","https://ap.wps.com/l/cbCaihI2TYlTxItO","pdf",310263,"English","# Limits and Continuity\n## Multiple-choice and True/False\n## Graph-based limit questions\n# Discontinuity and Asymptotes\n## Removable vs non-removable\n## Vertical asymptote identification\n# AP Test Questions\n## Approximation and solving based on tables\n## Function behavior and graph interpretation\n# Chapter One Test Problems","[{\"question\":\"How do you handle a limit when the function is undefined at the point?\",\"answer\":\"If f is undefined at x=c, the limit can still exist. The worksheet’s True/False item tests that the limit does not automatically fail just because f(c) is undefined.\"},{\"question\":\"What does it mean for a discontinuity to be removable vs non-removable?\",\"answer\":\"A removable discontinuity occurs when the function can be redefined at the point to match the limiting value. A non-removable discontinuity occurs when left/right behavior does not match or the limit does not settle to a single finite value.\"},{\"question\":\"How do you find vertical asymptotes from an expression for f(x)?\",\"answer\":\"Vertical asymptotes occur where the denominator goes to zero (and the function does not simplify to a finite value). The worksheet includes a multiple-choice problem asking which x-values produce vertical asymptotes.\"}]","AP Calculus AB - Chapter One Test | PDF",13]