[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523582-105":59,"doc-detail-523582-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","evaluating-limits-precalculus-worksheet","Evaluating Limits - Precalculus Worksheet","","This document provides a set of practice problems for evaluating mathematical limits, specifically designed for students studying precalculus. The worksheet includes various exercises requiring the evaluation of limits of functions, including rational functions and piecewise definitions. It features a critical thinking question that challenges students to construct an example of a rational function where a limit exists at a point even though the function is undefined there. This resource is suitable for classroom practice or independent study, focusing on the conceptual understanding of limits at removable discontinuities. The material is produced by Kuta Software as part of their Infinite Precalculus curriculum support tools.",{"@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/evaluating-limits-precalculus-worksheet/523582/",{"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/evaluating-limits-precalculus-worksheet/523582.png","ImageObject",300,407,{"name":92,"@type":93},"MrHarris58","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",11,{"@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 of various functions, including those with removable discontinuities.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What kind of critical thinking question is included?",{"text":118,"@type":114},"The question asks students to provide an example of a rational function where the limit at 3 exists, but the function is undefined at 3.",{"name":120,"@type":111,"acceptedAnswer":121},"Who created this document?",{"text":122,"@type":114},"The worksheet was created by Kuta Software for their Infinite Precalculus 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},523582,1791481679,{"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},687212988360,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Kuta Software-Infinite Precalculus Evaluating Limits  \nName  Date  Period   \nEvaluate each limit.  \n1) im􀁯 􀀗 f (x), f (x) = {􀀕􀀔 ,􀀐  \n􀀗x 􀀎 􀀗 , x  \nx  \n􀁺 􀀗  \n􀀠 􀀗  \n2)  \nlim  \nx􀁯 􀀐􀀗  \nx 􀀎 􀀗  \nx 􀀕 􀀎 􀀘x 􀀎 􀀗  \n3) im􀁯 􀀐􀀔 f (x), f (x) = {,􀀔 ,  \nx 􀀕 􀀐 􀀗  \n5) lim ~~  ~~x􀁯 􀀕 x 􀀐 􀀕  \nx 􀁺 􀀐􀀔  \nx 􀀠 􀀐􀀔  \n4) 􀀘 f (x), f (x) = {x,􀀕 􀀎 􀀔􀀓x 􀀐 􀀕􀀕 ,  \n6) im􀁯 􀀐􀀖 x~~ 􀀕 ~~x􀀎~~ ~~􀀎􀀘x􀀖􀀎~~ ~~􀀙~~ ~~  \nx 􀁺 􀀘  \nx 􀀠 􀀘  \nCritical thinking question:  \n7) Give an example of a limit of a rational function where the limit at 3 exists, but the function is undefined at 3.  \nKuta Software-Infinite Precalculus  \nEvaluating Limits  \nEvaluate each limit.  \n1) im􀁯 􀀗 f (x), f (x) = {􀀕􀀔 ,􀀐  \n􀀗x 􀀎 􀀗 , x  \nx  \n􀁺 􀀗  \n􀀠 􀀗  \n􀀗  \n3)  \n5)  \nlim  \nx􀁯 􀀐􀀔  \n􀀐􀀔  \nf (x), f (x) = {,􀀔 ,  \nim􀁯 􀀕  \nx 􀀕 􀀐 􀀗  \nx 􀀐 􀀕  \n􀀗  \nx 􀁺 􀀐􀀔  \nx 􀀠 􀀐􀀔  \nName  Date  Period   \n2)  \nlim  \nx􀁯 􀀐􀀗  \nx 􀀎 􀀗  \nx 􀀕 􀀎 􀀘x 􀀎 􀀗  \n􀀔   \n􀀐  \n􀀖  \n4) 􀀘 f (x), f (x) = {x,􀀕 􀀎 􀀔􀀓x 􀀐 􀀕􀀕 ,􀀖  \n6)  \nlim  \nx􀁯 􀀐􀀖  \nx 􀀎 􀀖  \nx 􀀕 􀀎 􀀘x 􀀎 􀀙  \n􀀐􀀔  \nx 􀁺 􀀘  \nx 􀀠 􀀘  \nCritical thinking question:  \n7) Give an example of a limit of a rational function where the limit at 3 exists, but the function is undefined at 3.  \nx 􀀕 􀀐 􀀜  \nMany answers. Ex: lim ~~ ~~  \nx􀁯 􀀖 x 􀀐 􀀖  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCainceexU5qX5w","https://ap.wps.com/l/cbCainceexU5qX5w","pdf",35856,"English","# Evaluating Limits\n## Practice Problems\n## Critical Thinking","[{\"question\":\"What is the primary focus of this worksheet?\",\"answer\":\"The worksheet focuses on evaluating limits of various functions, including those with removable discontinuities.\"},{\"question\":\"What kind of critical thinking question is included?\",\"answer\":\"The question asks students to provide an example of a rational function where the limit at 3 exists, but the function is undefined at 3.\"},{\"question\":\"Who created this document?\",\"answer\":\"The worksheet was created by Kuta Software for their Infinite Precalculus program.\"}]","Evaluating Limits - Precalculus Worksheet | PDF",1791427064]