[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-451866-105":59,"doc-detail-451866-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","ap-calculus-chapter-2-test","AP Calculus Chapter 2 Test","","AP Calculus Chapter 2 test covering key limit and continuity concepts for a function. Multiple-choice section emphasizes evaluating limits from graphs, identifying when limits exist or differ from one another, and determining continuity on intervals or at points. Free-response questions require computing algebraic and trigonometric limits, applying limit laws and the Intermediate Value Theorem, analyzing piecewise functions at boundary points, and using graph-based information to estimate tangents and rational-function asymptotes, domain, and range.",{"@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/ap-calculus-chapter-2-test/451866/",{"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-chapter-2-test/451866.png","ImageObject",300,407,{"name":92,"@type":93},"Finn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-25","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What topics are assessed in the multiple-choice section?","Question",{"text":113,"@type":114},"The multiple-choice section focuses on evaluating limits (often from graphs), testing continuity at points or intervals, determining limit behavior from one-sided limits, and selecting the correct tangent slope or asymptote-related outcome.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do the free-response questions test trigonometric limit skills?",{"text":118,"@type":114},"They ask students to compute trigonometric limits using known facts such as the standard limit involving sin x and then applying other limit properties to derive the requested results.",{"name":120,"@type":111,"acceptedAnswer":121},"What graph-related tasks appear in the later free-response questions?",{"text":122,"@type":114},"Students must sketch a function meeting specific limit/continuity conditions and also graph a rational function, then find its asymptotes (including non-standard/polynomial asymptotes), as well as its domain and range.","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},451866,1790794986,{"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":39,"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":46},34359740700684,"https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487","AP Calculus Chapter 2 Test  \nName:  Period:   \nPart I. Multiple-Choice Questions (5 points each)  \n1. The graph of a function f is given to the right.  \n(I) lim f (x) = 2 x! 1 􀀀  \n(II) lim f (x) = 􀀀1 x! 1+  \n(III) lim f(x) = 2 x!0  \n(A) I only  \n(B) II only  \n(C) I and II  \n(D) III only  \n(E) I, II, and III  \nPlace graphunit1   1 here  \nx2 􀀀 4x 􀀀 12  \n2. lim ~~   ~~ is x!􀀀 2+ px + 2  \n(A) = 0  \n(B) not de􀀌ned as the expression x2~~ ~~4x~~ ~~12 is not continuous at x = 􀀀2:  \n(C) = 1  \n(D) = 􀀀6  \n(E) = 6  \n3. De􀀌ne the function  \n8  1 􀀀 cos xf (x) = \u003C x  \n:0  \nThen  \nif x  0 if x = 0 :  \n(I) f is continuous on the set 􀀀1 \u003C x \u003C 1 .  \n(II) lim f (x) = 0 .  \nx!1  \n(III) lim f(x) = 0 x!0  \n(A) I only  \n(B) II only  \n(C) III only  \n(D) All are true  \n(E) None are true.  \nx2 + 5x 􀀀 6  \n4. The function f (x) = ~~   ~~  \npx 􀀀 1  \n(A) is continuous on the interval [1 ; 1 ) .  \n(B) is continuous on the whole real line.  \n(C) is continuous on [1 ; 1 ) provided that we de􀀌ne f (1) = 0  \n(D) is continuous on [1 ; 1 ) provided that we de􀀌ne f (1) = 7  \n(E) cannot be extended to a continuous function on [1 ; 1 )  \n5. The function f is de􀀌ned by setting f(x) = x + ~~1~~x . The slope of the line tangent to the graph of y = f(x) at the point (2; 2:5) is  \n(A) 0.5  \n(B) 0.25  \n(C) 􀀀0:75  \n(D) 0.75  \n(E) 􀀀0:5  \n6. The function f is de􀀌ned by setting f(x) = x + ~~1~~x . The slope of the line tangent to the graph of y = f(x) at the point (x; x + 1=x)  \n(I) approaches 0 as x ! +1 ;  \n(II) approaches 1 as x ! 􀀀1 ;  \n(III) approaches 􀀀1 as x ! 0+  \n(A) I only  \n(B) I and II  \n(C) II and III  \n(D) All are true  \n(E) None are true.  \n7. Assume that we have a continuous function g de􀀌ned on the interval [􀀀1; 3] such that f (􀀀1) = 3; f (0) = ~~1~~2 , f (2) = 􀀀2 and f (3) = 1 . Using the Intermediate Value Theorem we may conclude that  \n(I) g has a zero on the interval (􀀀1; 0);  \n(II) g has a zero on the interval (0 ; 2);  \n(III) g has a zero on the interval (2 ; 3);  \n(A) I only  \n(B) II only  \n(C) III only  \n(D) I and II  \n(E) II and III  \n8. Consider the function de􀀌ned by f (x) = x sin ~~1~~x . Then  \n(A) lim f(x) does not exist, but lim f (x) = 0 x!0 x!+1  \n(B) lim f(x) = +1 and lim f (x) = 0 x!0 x!+1  \n(C) lim f(x) = 1 and lim f (x) does not exist.  \nx!0 x!+1  \n(D) lim f(x) = 0 and lim f (x) = +1 x!0 x!+1  \n(E) lim f(x) = 0 and lim f (x) = 1 x!0 x!+1  \nPlace graph2 here  \n9. The diagram above depicts the graph of a rational function f. Judging from the graph,  \n(I) lim f (x) = +1 = lim f(x) x!􀀀 4 x!2  \n(II) lim f (x) = +1 = lim f(x) x!+1 x!2  \n(III) lim f (x) = 􀀀1 and lim f(x) = 0 x!􀀀 4+ x!0  \n(A) I only  \n(B) II only  \n(C) III only  \n(D) I and II  \n(E) II and III  \nPlace graph3 here  \n10. The diagram above depicts the graph of y = g(x) . Of the 􀀌ve choices given for the slope of the line tangent to the graph at the point (2; f (2)), which is the best?  \n(A) 􀀀1:9  \n(B) 1.9  \n(C) 0  \n(D) 􀀀3:1  \nPart II. Free-Response Questions  \n1. (3 points each) Compute the following limits 2x2 􀀀 7x + 3  \n(a) lim ~~  ~~x!3 x 􀀀 3  \npx + 1 􀀀 1  \n(b) lim ~~ ~~  \nx!0 x  \nx + px 􀀀 6  \n(c) lim ~~   ~~  \nx!4 px 􀀀 2 .  \nsin x  \n2. (3 points each) Using the fact that lim = 1, together with other properties  \nx!0 x  \nof the limit, compute the following trigonometric limits:  \ntan 2x  \n(a) lim  \nx!0 x  \n1 􀀀 cos2 x (b) lim ~~ ~~  \nx!0 x3 􀀀 x2  \nsin e􀀀x  \n(c) lim  \nx!+1 e􀀀x+1  \n3. (3 points) Let  \n8 x2 + x 􀀀 12  \nf (x) = \u003C x + 4 if x > 􀀀4  \n: 􀀀x 􀀀 11 if x 􀀔 􀀀4; and compute  \n(a) lim f (x) ; x!􀀀 4 􀀀  \n(b) lim f (x) ; x!􀀀 4+  \n(c) lim f (x) x!􀀀 4  \n4. (3 points each) Compute the limits below. (L; C, and k are constants, with  \nk > 0)  \nL  \n(a) x 1 + Ce􀀀kx  \n(b) lim  L  x!􀀀1 1 + Ce􀀀kx  \n5. (3 points) Sketch the graph of a function f satisfying the following conditions:  \n(a) The domain of f is [􀀀5; 5];  \n(b) lim f (x) exists; x!􀀀 2 􀀀  \n(c) lim f (x) = f(􀀀2) x!􀀀 2 􀀀  \n(d) lim f (x) exists; x!􀀀 2+  \n(e) lim f (x)  lim f (x) . x!􀀀 2 􀀀 x!􀀀 2+  \n\n| y 6\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>􀀛      |      - |\n| -","cbCaii8LhtH9z8hY","https://ap.wps.com/l/cbCaii8LhtH9z8hY","pdf",146281,"English","# Part I. Multiple-Choice Questions\n## Limits and continuity from graphs\n## Limit evaluation and function continuity\n## Tangent slopes and rational function behavior\n# Part II. Free-Response Questions\n## Computing limits (algebraic and trigonometric)\n## Piecewise function limits at points\n## Exponential limits and domain/range sketching\n## Rational-function limits, tangents, and asymptotes","[{\"question\":\"What topics are assessed in the multiple-choice section?\",\"answer\":\"The multiple-choice section focuses on evaluating limits (often from graphs), testing continuity at points or intervals, determining limit behavior from one-sided limits, and selecting the correct tangent slope or asymptote-related outcome.\"},{\"question\":\"How do the free-response questions test trigonometric limit skills?\",\"answer\":\"They ask students to compute trigonometric limits using known facts such as the standard limit involving sin x and then applying other limit properties to derive the requested results.\"},{\"question\":\"What graph-related tasks appear in the later free-response questions?\",\"answer\":\"Students must sketch a function meeting specific limit/continuity conditions and also graph a rational function, then find its asymptotes (including non-standard/polynomial asymptotes), as well as its domain and range.\"}]","AP Calculus Chapter 2 Test | PDF",1790736077]