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The problem collection is organized by core topics including limits and continuity, derivatives, local linear approximation and differentials, related rates, mean-value theorem, monotonicity/convexity and extrema, optimization, true/false items, and antiderivatives. 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The document explicitly indicates it is a “VERSION WITH ANSWERS,” and many problems are followed by answer lines.",{"name":120,"@type":111,"acceptedAnswer":121},"Is the content structured as a problem set by section?",{"text":122,"@type":114},"Yes. It lists numbered sections (e.g., Limits and Continuity, Derivatives, and others) and provides problems within each section, often labeled with problem numbers such as 1.1, 2.1, etc.","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},466345,1791057325,{"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":56,"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":145},2336477974920,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","CALCULUS I: FIU FINAL EXAM PROBLEM COLLECTION: VERSION WITH  \nANSWERS  \nFIU MATHEMATICS FACULTY NOVEMBER 2017  \nContents  \n1. Limits and Continuity 1  \n2. Derivatives 4  \n3. Local Linear Approximation and di􀀋erentials 6  \n4. Related Rates 7  \n5. Mean-Value Theorem 8  \n6. Monotonicity, Convexity, Local and Global Extrema, Graphs of functions 9  \n7. Optimization 12  \n8. True/False questions 14  \n9. Antiderivatives 18  \n1. Limits and Continuity  \nProblem 1.1. Use the graph of function f to 􀀌nd the limits  \n(1) lim f (x) = 􀀀5 (7) lim f (x) = 􀀀4 x!􀀀 3 􀀀 x!3 􀀀  \n(2) lim f (x) = 􀀀5 (8) lim f (x) = +1 x!􀀀 3+ x!3+  \n(3) xl3 f (x) = 􀀀5 (9) lxim!3 f (x) = d:n:e:  \n(4) lim f (x) = 4 (10) lim f (x) = 􀀀6 x!0 􀀀 x!􀀀 4 􀀀  \n(5) lim f (x) = 2 (11) lim f (x) = 􀀀6 x!0+ x!􀀀 4+  \n(6) lim f(x) = d:n:e: (12) lim f (x) = 􀀀6 x!0 x!􀀀 4  \nDate: 2018/04/14 .  \nCompiled on 2018/04/14 at 02:06:22 . Filaname: output.tex.  \n2 FIU MATHEMATICS FACULTY NOVEMBER 2017 Problem 1.2. Use the graph of function f to 􀀌nd the limits  \n(1) lim f (x) = +1 x!􀀀 3 􀀀  \n(2) lim f (x) = 􀀀4 x!􀀀 3+  \n(3) lim f (x) = d:n:e: x!􀀀 3  \n(4) lim f (x) = 2 x!0 􀀀  \n(5) lim f (x) = 4 x!0+  \n(6) lim f(x) = d:n:e: x!0  \n(7) lim f (x) = 􀀀5 x!3 􀀀  \n(8) lim f (x) = 􀀀5 x!3+  \n(9) lim f(x) = 􀀀5 x!3  \n(10) lim f (x) = 􀀀2 x!6 􀀀  \n(11) lim f (x) = 􀀀2 x!6+  \n(12) lim f(x) = 􀀀2 x!6  \nProblem 1.3. Find the limits. If the limit does not exist, then write dne  \n(1)  \n(2)  \n(3)  \n(4)  \n(5)  \n(6)  \n(7)  \n(8)  \n(9)  \n(10)  \n(11)  \n(12)  \n(13)  \nlim  \nx!2  \nlim  \nx!2  \nlim  \nx!2  \n2x2 􀀀3x+2  1 x2 +4x+4 = 4 ~~2x~~x~~2~~2~~x~~x = 0  \n~~2x~~x~~2~~2􀀀~~3~~􀀀4~~x~~x = +1  \nx ~~1~~1~~x~~3x~~2~~ = +1 lxim!3 x~~2~~12 = 􀀀108 lim 9􀀀x2 = 6  \nx!3 3􀀀x  \nlim  x􀀀3  = +1 x!6+ x2 􀀀x􀀀30 lim  x  = d:n:e:  \nx!2 j2􀀀xj  \nlim p2x2 􀀀3 = 􀀀 p2 x!􀀀1 x􀀀2  \nxl 􀀐 px2 + 2x 􀀀 x􀀑 = 1  \nxl 􀀐 px2 + 5 􀀀 x􀀑 = 0 lim cos􀀀1(ln x) = 􀀙 x! 1 2  \nlim 1􀀀cos(4x) = 0  \nx!0 x  \n(14)  \n(15)  \n(16)  \n(17)  \n(18)  \n(19)  \n(20)  \n(21)  \n(22)  \n(23)  \n(24)  \n(25)  \n(26)  \n(27)  \nxl ~~e~~2xx~~2~~ = +1  \nxl lne(2~~3~~x~~x~~) = 0  \nlim tan(4x) = 4 x!0 sin(3x) 3  \nlxim!0 xs(inx􀀀(x4))~~2 ~~ = 1~~1~~6 lim arcsin(3x) = 3  \nx!0 sin(x)  \nlim  x2  = 1  \nx!0 1􀀀cos2 x lim xe􀀀x = 0  \nx!1  \nlim xe􀀀x = 􀀀1 x!􀀀1  \nxl x sin 􀀀 ~~􀀙~~x 􀀁 = 􀀙 lim (tan(x) 􀀀 sec(x)) = 0  \nx! ( ~~􀀙~~2 ) 􀀀  \nlim (1 􀀀 tan x) sec(2x) = 1 x! ~~􀀙~~4  \nxlim!0+ 􀀀 ~~1~~x 􀀀 csc(x)􀀁 = 0 lim xx = 1  \nx!0+  \nlim (1 + 4x)1=x = e4  \nx!0+  \nCALCULUS I: FIU FINAL EXAM PROBLEM COLLECTION: VERSION WITH ANSWERS 3  \n8 0 ;  if x 􀀔 􀀀5  \nProblem 1.4 . Let f(x) = \u003C p25 􀀀 x2 ; if 􀀀 5 \u003C x \u003C 5 . Find the indicated limits  \n: 3x ; if x 􀀕 5  \n(1) lim f (x) = 0 (5) lim f (x) = 15  \nx!􀀀 5 􀀀 x!5+  \n(2) lim f (x) = 0 (6) lim f(x) = d.n.e.  \nx!􀀀 5+ x!5  \n(3) lim f (x) = 0 (7) Is f continuous at 5? Nox!􀀀 5 (8) Is f continuous at-5? Yes  \n(4) lim f (x) = 0 x!5 􀀀  \nProblem 1.5. Let f(x) = 􀀚  \n(1) lim f (x) =  4 x!􀀀1 5  \n(2) lim f (x) =  5 x!+1 4  \n 4x   \n5x+1  \n 5x   \n4x+1  \n;  \n;  \nif  \nif  \nx \u003C 1 000 000  \nx 􀀕 1 000 000  \n. Find the indicated limits  \n(3) Does the function have any asymptotes (horizontal or vertical)? If yes, provide the equation(s) .  \nAns.: yes, horizontal, y = ~~4~~5 ; y = ~~5~~4 , vertical x = 􀀀 ~~1~~5  \nProblem 1.6. Locate the discontinuities of the given functions. If there are none, then write \\none\"  \n(1) f (x) = x2x 􀀀 4 none (5) f (x) = p~~4~~x􀀀~~3~~2~~x~~ none in domain ( 􀀀1 ; ~~4~~3]((23)) ff((xx))  x2x~~2~~44 xn=on2; x = 2 (6) f (x) = px4􀀀􀀀2 3 ; none iif xn do1main ( 􀀀1 ; 43)  \n(4) f (x) = tan x x = (2k + 1)~~􀀙~~2 , k integer (7) f(x) = 􀀚 2x 􀀀x 1 ; if x􀀔> 1 x = 0 ; 1  \nProblem 1.7. Find the value of k so that the function f is continuous everywhere  \nf (x) = 􀀚 3xkx2+; k; if ifx 􀀔2 2  \nAns.: k = 2  \nProblem 1.8. Find the value of k so that the function f is continuous at x = 0  \nf (x) = ( tt2anank(xx;; iiff xx00  \nAns.: k = ~~3~~2  \nProblem 1.9. Given that lim f(x) = 3, and lim h (x) = 0, 􀀌nd the following limits  \nx! 1 x! 1  \na) lim h (x) = 0 x! 1 f (x)  \nb) lxim!1 (fh((xx)))~~2 ~~ = +1  \nProblem 1.10. Use the ","cbCaiciPEHY3KuYI","https://ap.wps.com/l/cbCaiciPEHY3KuYI","pdf",1236845,"English","# Limits and Continuity\n# Derivatives","[{\"question\":\"What topics are covered in the Calculus I final exam problem collection?\",\"answer\":\"It covers limits and continuity, derivatives, local linear approximation and differentials, related rates, the mean-value theorem, monotonicity/convexity and extrema, optimization, true/false questions, and antiderivatives.\"},{\"question\":\"Does the document include solutions or answer information?\",\"answer\":\"Yes. The document explicitly indicates it is a “VERSION WITH ANSWERS,” and many problems are followed by answer lines.\"},{\"question\":\"Is the content structured as a problem set by section?\",\"answer\":\"Yes. It lists numbered sections (e.g., Limits and Continuity, Derivatives, and others) and provides problems within each section, often labeled with problem numbers such as 1.1, 2.1, etc.\"}]","CALCULUS I: FIU FINAL EXAM PROBLEM COLLECTION - VERSION WITH ANSWERS | PDF",1790771097,48]