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Topics include Riemann sums and approximating areas under curves, differentiation rules (product/chain/implicit), definite integrals and the Fundamental Theorem, limits, and applications of related rates. Additional problems cover definite-integral properties, optimization of cost for a box, and a logic question on classifying increase/concavity at x=0. The second exam continues with integral linearity and motion/acceleration concepts.",{"@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-mac2311-final-exam-a-multiple-choice-review/466341/",{"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-mac2311-final-exam-a-multiple-choice-review/466341.png","ImageObject",300,407,{"name":92,"@type":93},"supergirl","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-24","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What question types are included in Final Exam A?","Question",{"text":113,"@type":114},"Final Exam A consists of multiple-choice questions covering Riemann sums, definite integrals, differentiation, limits, related rates, and conceptual statements about integral theorems.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do Riemann sum problems in this review specify the method?",{"text":118,"@type":114},"The problems specify the function, the interval, the number of subintervals, and whether to use left or right endpoints for the Riemann sum.",{"name":120,"@type":111,"acceptedAnswer":121},"What topics appear in Final Exam B based on the provided items?",{"text":122,"@type":114},"Final Exam B includes multiple-choice questions using linearity of definite integrals and a physics-style setup using acceleration to determine position at a given time.","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},466341,1791143414,{"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":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":145,"read_time":41},962088121634,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Calculus I: MAC2311 Name:    \nFinal Exam A  \nInstructions: multiple choice questions.  \n1. Approximate the area under the graph f (x) = 1 + sin2 (􀀙x) on the interval [0 ; 1=2] using a rightendpoint Riemann sum with 3 subintervals of equal length.  \n(A) 13 (B) 23 (C) 56 (D) 9~~ ~~+1p23 (E) 1  \n2. Given f0 (x) = ex + cos(x) and f (0) = 0, 􀀌nd f (x) .  \n(A) f (x) = ex + sin(x) 􀀀 1 (B) f (x) = ex + sin(x)  \n(C) f (x) = ex 􀀀 sin(x) 􀀀 1 (D) f (x) = ln(sin(x)) (E) none of the above  \n3. Consider the function f (x) = p3 􀀀 x. Which of the following is the de􀀌nition of f0 (􀀀1)?  \n0 p 3 􀀀 x 􀀀 2 0 p 3 􀀀 x 􀀀 2  \n(A) f (􀀀1) = lim ~~ ~~ (B) f (􀀀1) = lim ~~ ~~  \nx!􀀀 1 x + 1 x!1 x + 1  \n0 p 3 􀀀 x 􀀀 h 􀀀p 3 􀀀 x 0 h  \n(C) f (􀀀1) = lim ~~ ~~ (D) f (􀀀1) = lim ~~    ~~   \nh!0 h h!0 p 3 􀀀 x 􀀀 h 􀀀p 3 􀀀 x  \n4. Water 􀀍ows from the bottom of a storage tank at a rate r (t) = 200 􀀀 4t liters per minute, where 0 􀀔 t 􀀔 50. If at time t = 0 there are 5,000 gallons of water in the tank, how many of the following are true?  \n(i) Between the times t = 5 and t = 10, 850 gallons leave the tank  \n(ii) At t = 5, there are only 850 gallons still in the tank.  \n(iii) At t = 10, 1800 gallons have left the tank.  \n(iv) At t = 50, the tank is empty.  \n(A) 0 (B) 1 (C) 2 (D) 3 (E) 4  \n4  \n5. Evaluate Z 􀀒 3x + e 􀀁 e􀀀x 􀀀 x􀀀3=2􀀓 dx  \n1  \n 1   19  1   151  1   1   1   4 (A) ln(64) 􀀀 e3 (B) 􀀀 8 + e3 (C) 64 􀀀 e3 (D) ln(81) + 3e 􀀀 e4 (E) 3 ln(4) + e3 􀀀 3  \n6. Find Z sin(cos(x)) sin(x) dx.  \n(A) 􀀀 cos(sin(x)) + C (B) cos(sin(x)) + C (C) cos(cos(x)) + C (D) 􀀀 cos(cos(x)) + C (E) none of the abov  \n7. Evaluate lxim!0 x4 sin 􀀒 1x􀀓  \n(A) 1 (B) 0 (C) 1 (D) The limit does not exist  \n1 1  \n8. If Z f (x) dx =5 and Z g (x) dx = 􀀀3, which of the following must be true?  \n0 0  \n1  \n(i) Z f (x)g (x) dx = 􀀀15  \n0  \n1  \n(ii) Z [f(x) + g(x)]dx = 2  \n0  \n(iii) f (x) 􀀕 g(x) for all x in [0 ; 1]  \n(A) (i) and (ii) (B) (ii) (C) (iii) (D) (ii) and (iii) (E) (i), (ii), and (iii)  \n9. A ladder 13 ft long 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 angle that the ladder makes with the ground changing when the top of the ladder is 5 ft from the ground?  \n(A) 􀀀 15 (B) 􀀀 ~~ ~~11069 (C) 􀀀 16 (D) 􀀀 25  \n10. You are asked to 􀀌nd the minimal cost of materials to construct a rectangular storage container with an open top having a volume of 10 m3 . The length of the base is twice the width. Material for the base cost 15 per square meter, and material for the sides costs 5 per square meter. Let C represent the cost, w the width of the box, l the length of the box, and h the height of the box. Which of the following equations should you optimize to 􀀌nd the minimal cost of materials to construct the box?  \n(A) C = 15w0 + 30w2 (B) C = 15w0 + 60w2 (C) C = 30w + 2w2 (D) C = 30w + w2 (E) none of the above  \n11. Which of the following is the Riemann sum for the function f (x) = ln(x) over the interval [2; 4] using left-endpoints and 4 subintervals of equal length?  \n(A) i ln 􀀒 2 + 12i􀀓 12  \n(B) i ln 􀀒 2 + 12i􀀓 12  \n(C) i ln 􀀒 12i􀀓 12  \n(D) i ln 􀀒 12i􀀓 12  \n12. Find the values of m and k such that f (x) is continuous everywhere.  \n8  \n>  \nf (x) = \u003C>  \n:  \n2x3 + x + 7; x \u003C 􀀀1  \nm (x + 1) + k; 􀀀1 􀀔 x 􀀔 2  \nx2 + 2 ; 2 \u003C x  \n(A) m = 23 and k = 4 (B) m = 12 and k = 3 (C) m = 23 and k = 􀀀4 (D) m = 􀀀 23 and k = 􀀀4  \n13. Let f (x) = x2g(cos(2x)) . Find f0 (x) .  \n(A) 2xg(cos(2x)) 􀀀 2x2 sin(2x)g0 (cos(2x)) (B) 􀀀2xg0 (2 sin(2x))  \n(C) 2xg(cos(2x)) + x2 sin(2x)g0 (cos(2x)) (D) 2x 􀀀 2 sin(2x)g0 (cos(2x)) (E) none of the above  \n14. If xy 2 + 2xy = 8 then at the point (1 ; 2), y0 is  \n5  4  1  \n(A) 􀀀 (B) 􀀀 (C) 􀀀1 (D) 􀀀 (E) 0  \n2 3 2  \n15. The sum of two positive numbers is 16 . What is the smallest possible value of the sum of their squares?  \n(A) 128 (B) 162 (C) 130 (D) 256 (E) none of the above  \ne  \n16. Evaluate Z lnx(x)dx.  \n1  \n(A) 1 (B)  1  􀀀 1 (C) 1 (D) 0 (E) none of the above  \n3 e2 2  \n17. Evaluate lim x4 e􀀀x  \nx!1  \n(A) 0 (B) 24 (C) 1 (D) The lim","cbCaigTxSqyxoUcj","https://ap.wps.com/l/cbCaigTxSqyxoUcj","pdf",237834,12,"English","# Final Exam A\n## Riemann sums and definite integrals\n## Differentiation, limits, and applications\n## Series of true/false style reasoning\n# Final Exam B\n## Integral properties and acceleration problems","[{\"question\":\"What question types are included in Final Exam A?\",\"answer\":\"Final Exam A consists of multiple-choice questions covering Riemann sums, definite integrals, differentiation, limits, related rates, and conceptual statements about integral theorems.\"},{\"question\":\"How do Riemann sum problems in this review specify the method?\",\"answer\":\"The problems specify the function, the interval, the number of subintervals, and whether to use left or right endpoints for the Riemann sum.\"},{\"question\":\"What topics appear in Final Exam B based on the provided items?\",\"answer\":\"Final Exam B includes multiple-choice questions using linearity of definite integrals and a physics-style setup using acceleration to determine position at a given time.\"}]","Calculus I - MAC2311 Final Exam A - Multiple Choice Review | PDF",1790771090]