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Includes implicit differentiation, Newton’s Method for root approximation, linear approximation estimation, and applications of related rates for sphere and cylindrical volume problems. Further tasks involve critical points with extrema, Mean Value and Rolle’s Theorems, concavity analysis, integrals via substitution and the Fundamental Theorem of Calculus, area between curves, and extensive evaluation requiring L’Hôpital’s Rule where needed.",{"@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/math1131q-calculus-1-final-exam-review-session-practice-problems/466357/",{"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/math1131q-calculus-1-final-exam-review-session-practice-problems/466357.png","ImageObject",300,407,{"name":92,"@type":93},"Aran","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What types of limit problems are included in this review?","Question",{"text":113,"@type":114},"The review asks students to evaluate limits directly and determine whether limits exist, including problems that may require L’Hôpital’s Rule multiple times.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How are derivatives and tangents handled in the practice set?",{"text":118,"@type":114},"It includes taking derivatives of various functions, using implicit differentiation, and finding equations of tangent lines at given points.",{"name":120,"@type":111,"acceptedAnswer":121},"Which major integral topics and theorems are covered?",{"text":122,"@type":114},"The set covers evaluating integrals (including definite/area context), using the Fundamental Theorem of Calculus, and computing the area between two curves.","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},466357,1790812059,{"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":146},137455076865,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","# MATH1131Q:Calculus 1Final Exam Review Session\n\n04/30/2025  \n## 1 Practice Problems\n\n1.Evaluate the following limits or show they do not exist.  \n(a)  \n(b)  \n(c)  \n(d)  \n2.Evaluate the following limits:  \n(a)  \n(b)  \n3.Determine the asymptotes(both vertical and horizontal)of the following functions:  \n(a)  \n(b)  \n4.Consider the following function:  \nEvaluate limz→1-g(x),limx→1+9(x).Does the limx→19(x)exist?Is g(x)continuous at x=1?  \n   \n   \n5.Assume f,g are continuous function such that f(1)=3 and  \nFind the value of g(1).  \n6.Take the derivative of the following functions:  \n(a)f(x)=5x⁶eˣ+2ln(x)  \n(b)  \n(c)f(x)=em²tan(x)+6xln(x²+1)  \n7.Find the derivative y'(x)using implicit differentiation of  \n6x³e⁵ᵗ+2y²(x)+3y³(x)=-2xy(x)  \n8.Find the equation of the tangent line to the curve x³eᵗ+y²=4 at the point(0,2).  \n9.Determine the derivative of the following functions:  \n(a)f(x)=e3z+1+5x  \n(b)f(x)=5ᵗ+x²+x  \n10.The half-life of chromium-51 is about 28 days.Let M(t)be the mass of chromium-51 at a timet withinitial mass 100 kilograms(kg).Determine the formula for M(t),where t is the number of days.Afterhow much time will the initial mass shrink to 1 kg?  \n11.Determine the linear approximation of the function f(x)=3x³+1 at x=2 and use the approximationto estimate 28.5  \n12.A spherical balloon is inflating at a rate of 12π.How fast is the surface area of the balloon increasingwhen the radius of the balloon is 6 cm?  \n13.A cylindrical tank of radius 10 feet is being filled with water at a rate of 2 ft³/minute.How fast is thedepth of the water in the tank increasing?  \n14.Find the critical points and any absolute minima/maxima of the following function on the given interval:  \nf(x)=x³-3x+1,on [0,2].  \n15.Determine whether the following functions satisfy the conditions of the Mean Value Theorem:  \n(b)g(x)=x³-4x²+1 on [-1,2]  \n16.Determine wheter the following functions satisfy the conditions of Rolle's Theorem:  \n(a)  \non [-1,1]  \n(b)g(x)=3x²+3x+5 on [-2,1]  \n17.Find every number c that satisfies the conclusion of the Mean Value Theorem for  \nf(x)=x³-2x²+1  \non [0,1]  \n   \n   \n18.Find the critical points,maxima,minima,the intervals where f is increasing,decreasing,concave up,orconcave down for the following functions:  \n(a)f(x)=x⁴-2x²+3  \n(b)f(x)=x²-2x  \n19.Determine the following limits(you may need to use L'Hopital's Rule multiple times):  \n(a)  \n(b)  \n(c)  \n(d)  \n20.Use Newton's Method to approximate a root of f(x)=x⁴-5x+2 in [0,4].Let xo=1 and find thesolutions x1 and x2.  \n21.An open box needs to be constructed to have a volume of 40m³and a base whose width four times itslength.Determine the dimensions (length,width,height)of such a box that uses the least amount ofmaterials.  \n22.Determine the following integrals:  \n(a)ʃx²+1 dx  \n(b)ʃ2sin(x)dx  \n(c)e²+2 dx  \n(d)Jx²(3x-8)dx  \n23.Using the Fundamental Theorem of Calculus,evaluate the derivative of the integrals:  \n24.Evaluate the integral  \n25.Evaluate the area between the two curves f(x)=-1-4x and g(x)=x²+2.  \n①aauon  m o  showey w  \nu6-7 3-968P,2-23。  \nThis mans o Ty h srei you can farom anu sipeify khu taking a limit n myle wing LHopre.Nole,  \nx²-9=(x-3)(x+3)8,  \n   \n2³-qx²+2Fx-21=(x-3)³  \n   \n   \npugng in os  X55-与=5  and (525.2525=h  i hi ent  \nTy fuctring:5x-25=(5z)²-s²=(B-5)(5+5)TZoum  \n   \n   \n   \nDNE  \nx\u003C1,x³+3x-4\u003C0.  \nfn  \nbeuauu  \n8ohu lim't does nol eust(DNE).  \n   \n   \n②eacnce u owi m  \n(0r uih mou dutuil)  \n   \n   \n③ami  yuial oiomae   mins  \nVuhiol Asympohtr  \nThem,x²-5x+6=0→(x-2)(x-3)=0今x=Q,x=3.Mok Mat neinu x=2nn x=3 au Ae of x+4.fx)haJ wuhal adympbhky at x=2 and x=3Thw,  \n   \n   \n   \n   \n   \n   \n   \nHorintra ymorr.n  oe y cun mut →t0 ,e tae  and     \nm l = i  \nfa) hur a hoizmhul asympble  \n0  \n.Check wheu hu deno minu ton gouy加0.  \nou luaduubic Fnmula  \nhas arae ayoo a   2 and x=-  \nHorinta ymt.n  hoe cun mat  00, e  tale  \nhi fu5-4≈1 322  \n④wg ho  \nI fx) conhnuouo at d=1?  \nx+4→f(x1 = limm  \nfa=e  \nBut fl1)=4,and 4≠-6,  \nfo  \n→  \n n  conhnuous  =  \n③     at fu=. en ","cbCaivXiHSSeMbJV","https://ap.wps.com/l/cbCaivXiHSSeMbJV","pdf",30392654,15,"English","# 1 Practice Problems\n## Limits and Asymptotes\n## Continuity and Derivatives\n## Applications (Linear Approximation, Related Rates)\n## Theorems (Mean Value, Rolle’s)\n## Critical Points and Concavity\n## Integrals and Area Between Curves\n## Numerical Methods (Newton’s Method)","[{\"question\":\"What types of limit problems are included in this review?\",\"answer\":\"The review asks students to evaluate limits directly and determine whether limits exist, including problems that may require L’Hôpital’s Rule multiple times.\"},{\"question\":\"How are derivatives and tangents handled in the practice set?\",\"answer\":\"It includes taking derivatives of various functions, using implicit differentiation, and finding equations of tangent lines at given points.\"},{\"question\":\"Which major integral topics and theorems are covered?\",\"answer\":\"The set covers evaluating integrals (including definite/area context), using the Fundamental Theorem of Calculus, and computing the area between two curves.\"}]","MATH1131Q: Calculus 1 Final Exam Review Session - Practice Problems | PDF",1790771115,38]