[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522869-105":59,"doc-detail-522869-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","limits-in-form-of-definition-of-derivative-calculus-practice-exercises","Limits in Form of Definition of Derivative - Calculus Practice Exercises","","This calculus worksheet, developed by Kuta Software for their Infinite Calculus program, presents a series of mathematical limit problems specifically designed to practice the definition of the derivative. Students are tasked with evaluating six distinct limit expressions, which involve polynomial and trigonometric functions. The document serves as an educational tool for students to master the fundamental calculus concept of the difference quotient and its application in formal differentiation. Each problem is structured to challenge learners on the algebraic manipulation of limits in the form of f(x+h) - f(x) over h as h approaches zero, encouraging rigorous practice of core calculus principles.",{"@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/limits-in-form-of-definition-of-derivative-calculus-practice-exercises/522869/",{"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/limits-in-form-of-definition-of-derivative-calculus-practice-exercises/522869.png","ImageObject",300,407,{"name":92,"@type":93},"Angel","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",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 is the primary focus of this worksheet?","Question",{"text":113,"@type":114},"The worksheet focuses on evaluating limits that are presented in the form of the definition of the derivative.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How many problems are included in the exercise set?",{"text":118,"@type":114},"There are 6 distinct limit evaluation problems provided in this worksheet.",{"name":120,"@type":111,"acceptedAnswer":121},"Who is the developer of this calculus worksheet?",{"text":122,"@type":114},"This worksheet was created using Kuta Software's Infinite Calculus program.","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},522869,1791519013,{"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":14,"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":24,"preview_page_count":4},687207412472,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Kuta Software-Infinite Calculus  \nLimits in Form of Definition of Derivative  \nName  Date  Period   \nEvaluate each limit.  \n1) im􀁯 􀀓  (~~ ~~􀀗􀀖 􀀎 h 􀀐 (~~ ~~􀀗􀀖~~ ~~) 􀀕  \n3)  \n5)  \nim􀁯 􀀓  \nim􀁯 􀀓  \n( 􀀐 ~~ ~~􀀔􀀕 􀀎 h) 􀀕 􀀐 ( 􀀐 ~~ ~~􀀔􀀕~~ ~~) 􀀕  \nh  \nsin (~~ ~~~~ ~~ 􀀎 h) 􀀐 sin ~~ ~~~~ ~~  \nh  \n2) im􀁯 􀀓  (~~ ~~􀀔􀀕 􀀎 h 􀀐 (~~ ~~􀀔􀀕~~ ~~) 􀀖   \n4) im􀁯 􀀓 􀀕 ( 􀀐 ~~ ~~􀀕􀀖 􀀎 h) 􀀗h􀀐 􀀕 􀂘 ( 􀀐 ~~ ~~􀀕􀀖~~ ~~) 􀀗  \n6) im􀁯 􀀓  ( 􀀐 ~~ ~~􀀔􀀖 􀀎 hh) 􀀗 􀀐 􀀛􀀔􀀔~~ ~~  \nKuta Software-Infinite Calculus  \nLimits in Form of Definition of Derivative  \nName  Date  Period   \nEvaluate each limit.  \n1) im􀁯 􀀓  (~~ ~~􀀗􀀖 􀀎 h 􀀐 (~~ ~~􀀗􀀖~~ ~~) 􀀕  \n􀀛   \n􀀖  \n3) im􀁯 􀀓  ( 􀀐 ~~ ~~􀀔􀀕 􀀎 h 􀀐 ( 􀀐 ~~ ~~􀀔􀀕~~ ~~) 􀀕  \n􀀐􀀔  \n5) im􀁯 􀀓  sin (~~ ~~~~ ~~ 􀀎 hh) 􀀐 sin ~~ ~~~~ ~~   \n􀀕  \n􀀕  \n2) im􀁯 􀀓  (~~ ~~􀀔􀀕 􀀎 h 􀀐 (~~ ~~􀀔􀀕~~ ~~) 􀀖   \n􀀖   \n􀀗  \n4) im􀁯 􀀓 􀀕 ( 􀀐 ~~ ~~􀀕􀀖 􀀎 h) 􀀗h􀀐 􀀕 􀂘 ( 􀀐 ~~ ~~􀀕􀀖~~ ~~) 􀀗  \n􀀙􀀗  \n􀀐  \n􀀕􀀚  \n6) im􀁯 􀀓  ( 􀀐 ~~ ~~􀀔􀀖 􀀎 hh) 􀀗 􀀐 􀀛􀀔􀀔~~ ~~  \n 􀀗   \n􀀐  \n􀀕􀀚  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCailHlCDM3oa6g","https://ap.wps.com/l/cbCailHlCDM3oa6g","pdf",29882,"English","# Practice Problems\n## Limit Evaluation Exercises","[{\"question\":\"What is the primary focus of this worksheet?\",\"answer\":\"The worksheet focuses on evaluating limits that are presented in the form of the definition of the derivative.\"},{\"question\":\"How many problems are included in the exercise set?\",\"answer\":\"There are 6 distinct limit evaluation problems provided in this worksheet.\"},{\"question\":\"Who is the developer of this calculus worksheet?\",\"answer\":\"This worksheet was created using Kuta Software's Infinite Calculus program.\"}]","Limits in Form of Definition of Derivative - Calculus Practice Exercises | PDF",1791426253]