[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-463354-105":59,"doc-detail-463354-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","math-220-practice-exam-1","Math 220 - Practice Exam 1","","This document serves as a comprehensive practice exam for a Calculus course, specifically identified as Math 220. It covers fundamental topics including the calculation of limits, differentiation techniques for various functional forms, the application of differentials for approximations, implicit differentiation to find tangent lines, and related rates problems involving physical scenarios. The exam also provides a table of function values and derivatives at specific points to test the application of the chain rule. This resource is designed for students preparing for examinations by challenging them with problems that span from limit evaluation to complex rate-of-change analysis in real-world contexts. It provides a structured set of exercises that allow students to reinforce their mathematical proficiency and analytical skills ahead of their formal assessment.",{"@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/math-220-practice-exam-1/463354/",{"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/math-220-practice-exam-1/463354.png","ImageObject",300,407,{"name":92,"@type":93},"Melati","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","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},"How do you find the differential of a function f(x) at a specific point?","Question",{"text":112,"@type":113},"The differential df is calculated as f'(x)dx. To approximate f(x) near a known point, you use the formula f(x+dx) ≈ f(x) + f'(x)dx.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the approach for solving a related rates problem involving a ladder?",{"text":117,"@type":113},"Set up an equation using the Pythagorean theorem, x² + y² = 10², differentiate both sides with respect to time (t), and solve for dy/dt using the given rate dx/dt and the specific position of the ladder.",{"name":119,"@type":110,"acceptedAnswer":120},"How are the chain rule problems solved using the provided table?",{"text":121,"@type":113},"For composite functions like h(x) = f(g(x)), apply the chain rule formula h'(x) = f'(g(x)) * g'(x), then substitute the values for x, g(x), and their derivatives as provided in the reference table.","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},463354,1790766453,{"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":14,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":24,"preview_page_count":4},962085570644,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Math 220-Practice Exam 1  \n1. Give the limit if it exists  \n(a) limx!2 􀀀 jx2x􀀀22x~~ ~~j  \n(b) limx!2+ jx2x􀀀22x~~ ~~j  \n(c) limx!2 p~~x~~x~~2~~2􀀀~~2~~  \n2. Determine the derivatives of the following functions:  \n(a) f (x) = x4 􀀀 2 px + 1 􀀀 ~~2~~x~~3~~ + 􀀙x 􀀙 ;  \n(b) f (x) = (x2 􀀀 4x + 5)6 (2x3 􀀀 1)3 ;  \n(c) g (x) = (x􀀀si~~3~~n(x))~~2~~ ;  \n(d) f (x) = sin1c)toas~~2~~n((3x)x) ;  \n(e) h (x) = sin3 (x3 ) :  \n3. Evaluate the limit  \ntan(􀀙=4 + h) 􀀀 1 lim :  \nh!0 h  \n4. If f(x) = x3 􀀀 2x + 1,  \n(a) What is the di􀀋erential of f (x) at x = 2?  \n(b) f (2) = 5 . Use the di􀀋erential to approximate f (1:9) .  \n5. Use implicit di􀀋erentiation to determine the equation of the tangent line to the curve x3 y 2 􀀀 x2 y3 + 2x2 􀀀 y 2 = 1  \nat the point (1 ; 1) .  \n6. A 10m ladder leans against a wall. As the base of the ladder is pulled away at a rate of 0:6m=s, the ladder slides down the wall. At what rate is the height of the top of the ladder changing when the base of the ladder is 6m from the wall? (Give an exact numerical answer)  \n7. Determine where the function f(x) = xp8 􀀀 x2 has a horizontal tangent line.  \n8. Sketch the graph of the derivative of the given function f (x):  \n9. The chart below gives the values of f (x) and g(x) and their derivatives at x = 2, x = 3 and x = 4 .  \n\n|  | f (x) | g (x) | f 0 (x) | g0 (x) |\n| --- | --- | --- | --- | --- |\n| 2 | 4 | -2 | 3 | 9 |\n| 3 | 0 | 29 | -1 | 4 |\n| 4 | 3 | 2 | 7 | 11 |\n\nUse it to 􀀌nd the following derivatives,(a) If h (x) = f(g(x)), determine h0 (4) .  \n(b) If k (x) = g(f(x)), determine k0 (4) .","cbCaiboAx73J2x5q","https://ap.wps.com/l/cbCaiboAx73J2x5q","pdf",110922,"English","# Limit Problems\n# Differentiation Exercises\n# Limit Evaluation\n# Differential Approximation\n# Implicit Differentiation\n# Related Rates - Ladder Problem\n# Horizontal Tangent Lines\n# Derivative Graphing\n# Function and Derivative Table Analysis","[{\"question\":\"How do you find the differential of a function f(x) at a specific point?\",\"answer\":\"The differential df is calculated as f'(x)dx. To approximate f(x) near a known point, you use the formula f(x+dx) ≈ f(x) + f'(x)dx.\"},{\"question\":\"What is the approach for solving a related rates problem involving a ladder?\",\"answer\":\"Set up an equation using the Pythagorean theorem, x² + y² = 10², differentiate both sides with respect to time (t), and solve for dy/dt using the given rate dx/dt and the specific position of the ladder.\"},{\"question\":\"How are the chain rule problems solved using the provided table?\",\"answer\":\"For composite functions like h(x) = f(g(x)), apply the chain rule formula h'(x) = f'(g(x)) * g'(x), then substitute the values for x, g(x), and their derivatives as provided in the reference table.\"}]","Math 220 - Practice Exam 1 | PDF"]