[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-466348-105":59,"doc-detail-466348-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","calculus-i-final-exam-practice-problems-fordham-math-1206","Calculus I Final Exam Practice Problems - Fordham Math 1206","","This document provides a comprehensive set of practice problems for the Calculus I Final Exam at Fordham University (Math 1206). It includes ten multipart questions covering fundamental calculus concepts such as limits, continuity, the Intermediate Value Theorem, the definition of the derivative, various differentiation techniques including implicit and logarithmic differentiation, tangent lines, related rates problems involving conical piles, linear approximation using differentials, the Extreme Value Theorem, and the Mean Value Theorem.",{"@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/calculus-i-final-exam-practice-problems-fordham-math-1206/466348/",{"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-final-exam-practice-problems-fordham-math-1206/466348.png","ImageObject",300,407,{"name":92,"@type":93},"Grenda","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-28","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What specific calculus theorems are covered in this practice set?","Question",{"text":112,"@type":113},"The document covers the Intermediate Value Theorem, the Extreme Value Theorem, and the Mean Value Theorem, including their hypotheses and applications.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Are there problems involving related rates?",{"text":117,"@type":113},"Yes, problem 7 requires students to calculate the rate at which the height of a conical pile of gravel increases given a constant dumping rate.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the date and time for the final exam mentioned in the supplementary note?",{"text":121,"@type":113},"The final exam is scheduled for Tuesday, December 15th, from 1:30 PM to 3:30 PM via Zoom.","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},466348,1790771101,{"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":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"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":129,"read_time":144},7971474921005,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Fordham Math 1206, Calculus I Final Exam Practice Problems  \n1. Find the limit or state that it does not exist. Justify your answer.  \n(a) xl ⇣ px2 +2x −px2 − x⌘  \n(b) lim (ln(1/x) − ln(1/sin4x)) x!0+  \n(c) lim sin x  \nx!1 ln x  \n2. Find a and b such that the following function is continuous on R.  \n8 (x − 1)2 f (x) = \u003C ax + b : p2x +1  \nif x \u003C 1  \nif 1 􀀢 x 􀀢 4  \nif x > 4  \n3. (a) State the Intermediate Value Theorem, including the hypotheses.  \n(b) Prove that the following equation has at least one real solution. px − 5 = x~~ ~~~~ ~~3  \nPage 3  \n4. Let f (x) = 23x . Use the definition of the derivative as a limit to find f 0 (x) .   \n5. Find dy dx .  \n(a) y = sin(x2 )cos4 ( px)(2x5 − 1)4 (3x4 + 5)3  \n(b) y = ~~    ~~px2 +1  \n(c) xy = yx  \n(d) y = Z0tan x p1 − t3 dt  \n6. Find the tangent line to the curve y = sin(⇡x)e − x at the point (2 , 0) .  \n7. Gravel is being dumped from a conveyer belt at a rate 30 cubic feet per minute, and its courseness is such that it forms a pile in the shape of a cone whose base diameter and height are equal. How fast is the height of the pile increasing when the pile is 10 feet tall?  \n8. Use di↵erentials/linear approximation to estimate sin(⇡/6 + 0 .01) . You do not need to simplify your  \nanswer.  \n9. (a) State the Extreme Value Theorem, including the hypotheses.   \n px   \n(b) Find the absolute maximum and absolute minimum value of f(x) = 1+ x2 over the interval [0 , 2]  \n10. (a) State the Mean Value Theorem, including the hypotheses.  \n(b) Suppose f(x) is a di↵erentiable function such that f(1) = 2 and f 0 (x) ≥ 5 for all x. What is the smallest possible value for f(4)? Justify your answer.","cbCaii2hcZbk69c2","https://ap.wps.com/l/cbCaii2hcZbk69c2","pdf",4682039,14,"English","# Calculus I Final Exam Practice Problems\n## Limits and Continuity\n## Theorems and Proofs\n## Derivatives and Differentiation\n## Applications of Differentiation","[{\"question\":\"What specific calculus theorems are covered in this practice set?\",\"answer\":\"The document covers the Intermediate Value Theorem, the Extreme Value Theorem, and the Mean Value Theorem, including their hypotheses and applications.\"},{\"question\":\"Are there problems involving related rates?\",\"answer\":\"Yes, problem 7 requires students to calculate the rate at which the height of a conical pile of gravel increases given a constant dumping rate.\"},{\"question\":\"What is the date and time for the final exam mentioned in the supplementary note?\",\"answer\":\"The final exam is scheduled for Tuesday, December 15th, from 1:30 PM to 3:30 PM via Zoom.\"}]","Calculus I Final Exam Practice Problems - Fordham Math 1206 | PDF",35]