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The materials include questions based on a given graph and functions evaluated at specific x-values, followed by multiple limit problems involving one-sided limits, infinite behavior, and cases where limits do or do not exist (including DNE and infinity forms). Additional items apply continuity via the definition at points of discontinuity, and request analysis of removable versus nonremovable discontinuities, vertical asymptotes, and related true/false statements.",{"@graph":69,"@context":122},[70,84,105],{"@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/ap-calculus-ab-unit-1-12-16-review-limits-solutions/459798/",{"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/ap-calculus-ab-unit-1-12-16-review-limits-solutions/459798.png","ImageObject",300,407,{"name":92,"@type":93},"LangkahRina","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What topics are covered in this Unit 1 review?","Question",{"text":112,"@type":113},"The review focuses on evaluating limits and applying the definition of continuity, including removable and nonremovable discontinuities, vertical asymptotes, and when limits do not exist (DNE).","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"When are calculators allowed in the solutions set?",{"text":117,"@type":113},"Calculators are not allowed for Part I (Problems 1-37). Calculators may be used on the first part of Part II of the section.",{"name":119,"@type":110,"acceptedAnswer":120},"How does the document handle points where the function is undefined or discontinuous?",{"text":121,"@type":113},"It distinguishes cases where the limit exists but the function value does not (removable discontinuity) and cases involving one-sided limits or where the limit does not exist (DNE), using specific x-values and continuity checks.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},459798,1790756931,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":24,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143,"preview_page_count":4},962090893776,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","AP Calculus AB Name:  Solutions   \nUnit 1 (1.2-1.6) Review-LIMITS  \nPART I- DO NOT USE A CALCULATOR ON ANY PROBLEM IN THIS SECTION. (Problems 1-37)  \nConsider the graph of function, f , shown below.  \n|  |  |  |  |  |  |  |  |  |  |  | 6 | |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | f |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  | 4 |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  | 2 |  |  |  |  |  |  |  |  |  |  |  |  |\n| |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  | -1 | 0 |  |  |  | - | 5 |  |  |  |  |  |  |  |  | 5 |  |  |  |  | 1 | \u003Cbr>0 |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  | -2 |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  | -4 |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\nAnswer the following questions about function f.  \n1.) f (-5) = 6 2.) f (2) = 1 3.) f (4) = -3  \n4.) lim f (x) = 2 5.) lim f (x) = 6 6.) limf (x) = 3 x®-7 x®-5 x®2  \n7.) limf (x) = DNE 8.) limf (x) = DNE 9.) lim f (x) = -¥DNEx®4 x®0 -  \nx®0  \n10.) lim f (x) = +¥ DNE 11.) lim f (x) = -3 12.) lim f (x) = 2  \nx®0+ x®4+ x®4-  \n13.) lim f (x) =0+ 14.) limf (x) =0-  \nx®-¥ x®¥  \n15.) Use the definition of a continuous function at a number to answer the following.  \na. f is not continuous at x = -7 because:__f (-7 ) is not defined   \nb. f is not continuous at x = 2 because:  f (2 )¹ limx®2 f (x )   \nc. f is not continuous at x = 4 because:  limf (x) = DNE  x®4  \nDO NOT USE A CALCULATOR  \n\n| 16.) limx®2 (-x2 + 4x)\u003Cbr>= (- (2 )2 + 4(2 ))= 4 |  | x-3 ìï9-3 17.) lim ~~ ~~ í\u003Cbr>x®9- x-9 ïî9-9 = Do some algebra\u003Cbr>= lim x®9-\u003Cbr>x\u003Cbr>é   ùê ~~ ~~ ~~   ~~ úêë  ûú\u003Cbr>\u003Cbr>-3 x-9\u003Cbr>x\u003Cbr>\u003Cbr>+3 x\u003Cbr>\u003Cbr>+3 | = 0 0 | x ì0\u003Cbr>18.) lim ~~ ~~ í x®0 tan x îtan0 = 0\u003Cbr>Do some algebra\u003Cbr>= limx®0 êéësixnx~~ ~~cos1x~~ ~~ ùûú= (1)(1)= 1 |\n| --- | --- | --- | --- | --- |\n|  |  | = lim x®9-\u003Cbr>éêêêë\u003Cbr>ù x-9 ú(x-9 )( x +3)ûú\u003Cbr>= lim x®9-\u003Cbr>é 1 ù\u003Cbr>ê ú\u003Cbr>ë x +3 û\u003Cbr>=\u003Cbr>1 6-\u003Cbr>|  |  |\n| 19.) lim x→−2+ | 􀂧 x 􀂷􀂨 ~~ ~~ 􀂸􀂩 x+ 2 􀂹 | 􀂧  1 􀂷\u003Cbr>20.) lx0 − 􀂩􀂨 1+ x 􀂹􀂸\u003Cbr>æ  1 ö\u003Cbr>= çè1 + 0- ø÷ = -¥ DNE |  | 21.) lixm®1 (sinpx )\u003Cbr>= (sinp(1))= 0 |\n| æ  -2+ ö  -2+\u003Cbr>= èç -2 + + 2 ø÷ = 0 + = -¥ DNE |  |  |  |  |\n| 7 − 6x5\u003Cbr>22.) lim ~~  ~~x→􀁦 x+ 3\u003Cbr>= lxim®¥ ~~ ~~-6xx5 = lxim®¥ (-6x4 ) = -¥ DNE |  |  6-t 3  23.) tli®m- ¥ 7t3 +3\u003Cbr>-t3 1\u003Cbr>= lim ~~ ~~ = - ~~ ~~t®-¥ 7t3 7 |  | 24.) lim  x-2  x®-¥ x 2 + 2x +1\u003Cbr>x 1\u003Cbr>= lim ~~ ~~ = lim ~~  ~~x®-¥ x 2 + 2x x®-¥ x + 2  1  -\u003Cbr>= = 0 -¥ |\n| 2 − y\u003Cbr>25.) lim ~~   ~~y→−􀁦 7 + 6y2\u003Cbr>−y −y\u003Cbr>= lim ~~ ~~ = lim ~~ ~~y→−􀁦 6y2  y→−􀁦 y 6  1 \u003Cbr>=\u003Cbr> 6 |  | 26.) 2 f (x) when\u003Cbr>􀂭 x2 − 3x+ 6, x 􀀟 2 f (x) = 􀂮 2\u003Cbr>􀂯−x + 3x+ 2, x 􀁴 2 lxim®2-f (x )= 22-3(2 )+6 = 4 lxim®2+ f (x )= -22 +3(2 )+ 2 = 4 limx®2 f (x )= 4 |  | x2 − a2\u003Cbr>27.) If a 􀁺 0, then lxa x4 − a4 is:\u003Cbr>x 2-a2 ìï (-a )2-a2 = 0\u003Cbr>lim í\u003Cbr>x® -a x 4-a4 îï(-a )4-a4 = 0\u003Cbr>Do some algebra\u003Cbr> x 2-a2  lxim®-a (x 2-a2 )(x 2 + a2 )\u003Cbr>1 1\u003Cbr>= lim ~~ ~~ = ~~  ~~x®-a 1 (x 2 + a2 ) 2a2 |\n\n\n| 28.) Find a c such that f (x) is continuous on the entire real line. |  |  | 29.) Find the x-values (if any) at which f is discontinuous. Label as removable or nonremovable.\u003Cbr>f (x )= 22xx2~~ ~~+-618\u003Cbr>f (x )= 22xx2~~ ~~~~ ~~618 = xx2~~ ~~+-39 x +3 1\u003Cbr>= ~~ ~~ = ~~ ~~\u003Cbr>(x +3)(x-3) x-3 f (x ) is not defined at x = -3 xli®m-3+ f (x )= xli®m-3+ f (x )= - ~~ ~~16 removable discontinuity at x = -3 because the limit exists but the function value does not. |  |  | 30.) Determine all of the vertical asymptotes of f(x):\u003Cbr>f (x) = xx2~~ ~~24\u003Cbr>x + 2 1","cbCaiqdtwGmKzX07","https://ap.wps.com/l/cbCaiqdtwGmKzX07","pdf",553535,"English","# Unit 1 (1.2-1.6) Review - Limits - Solutions\n## Part I: No Calculator (Problems 1-37)\n## Part II: Calculators Allowed (First Part of Section)","[{\"question\":\"What topics are covered in this Unit 1 review?\",\"answer\":\"The review focuses on evaluating limits and applying the definition of continuity, including removable and nonremovable discontinuities, vertical asymptotes, and when limits do not exist (DNE).\"},{\"question\":\"When are calculators allowed in the solutions set?\",\"answer\":\"Calculators are not allowed for Part I (Problems 1-37). Calculators may be used on the first part of Part II of the section.\"},{\"question\":\"How does the document handle points where the function is undefined or discontinuous?\",\"answer\":\"It distinguishes cases where the limit exists but the function value does not (removable discontinuity) and cases involving one-sided limits or where the limit does not exist (DNE), using specific x-values and continuity checks.\"}]","AP Calculus AB Unit 1 - 1.2-1.6 Review - Limits - Solutions | PDF",13]