[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523581-105":59,"doc-detail-523581-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","Evaluating Limits","","Evaluate each limit in a worksheet format from Infinite Precalculus. Problems present piecewise functions and expressions as x approaches specified values, including cases where a limit does not exist. Several items encourage using a provided graph to sketch the function before determining the limit. The set culminates in a critical thinking prompt requiring writing a custom piecewise function that matches given limit and value conditions at a target input.",{"@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/523581/",{"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/523581.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 main task of the worksheet?","Question",{"text":113,"@type":114},"Evaluate each listed limit, often involving piecewise functions and approaching specific x-values.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How should you handle questions that mention a graph?",{"text":118,"@type":114},"Use the provided graph to sketch the function so the limit as x approaches the given value can be determined.",{"name":120,"@type":111,"acceptedAnswer":121},"What does the critical thinking question require?",{"text":122,"@type":114},"Write a piecewise function that satisfies specified limit behavior as x approaches a value and the function’s value at a particular input.","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},523581,1791518886,{"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":19,"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":52,"preview_page_count":4},687212988360,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Kuta Software-Infinite Precalculus Evaluating Limits  \nEvaluate each limit.  \n1) 􀀖􀀎 f (x), f (x) = {􀀐xx􀀕􀀐􀀎􀀖􀀗, x 􀀐 􀀖 ,  \nx  \nx  \n3)  \nlim  \nx􀁯 􀀐􀀕  \nf (x), f (x) = {􀀐􀀔􀀕x, 􀀐 􀀜 , xx 􀀟􀁴 􀀐􀀕􀀕  \nName  Date  Period   \n􀁤 􀀖  \n􀀡 􀀖  \n2)  \nlim  \nx􀁯 􀀖 􀀐  \n􀀖  􀀐x 􀀎 􀀖  \n􀀐x 􀀎 􀀖  \n4)  \nim􀁯 􀀕 f (x), f (x) = {􀀐  􀀕􀀔,, xx 􀁤􀀡 􀀕􀀕  \nEvaluate each limit. You may use the provided graph to sketch the function.  \n5)  \nxm􀀐􀀔 􀀐 f (x), f (x) = { ~~ ~~ 􀀕􀀐,  \nx 􀁤  \n􀀗 , x 􀀡  \n􀀐􀀔  \n􀀐􀀔  \n6)  \nim􀁯 􀀐􀀕 f (x), f (x) = {􀀕􀀎  ,􀀎 􀀛 ,  \nx  \nx  \n􀀟 􀀐􀀕  \n􀁴 􀀐􀀕  \nEvaluate each limit.  \n7)  \n9)  \nlim  \nx􀁯 􀀗 􀀐  \nlim  \nx􀁯 􀀔 􀀎  \nf (x), f (x) = {􀀘􀀎  ,  \nx 􀀟 􀀗  \nx 􀁴 􀀗  \nf (x), f (x) = {x􀀐􀀐􀀗 􀀘, ,  \nx 􀀟 􀀔  \nx 􀁴 􀀔  \n8)  \n􀀖􀀐 f (x), f (x) = {x  ,􀀗x 􀀐  \n10)  \nlim  \nx􀁯 􀀐􀀖 􀀐  \nf (x), f (x) = {􀀐 􀀐 􀀗x  \n􀀖 , x 􀀟 􀀖 x 􀁴 􀀖  \n􀀐 􀀗 , x 􀀟 􀀐􀀖 x 􀁴 􀀐􀀖  \nCritical thinking question:  \n11) Write a piecewise function where 􀀕 􀀐 f (x) 􀀠 􀀔 ,  \nlim  \nx􀁯 􀀕 􀀎  \nf (x) 􀀠 􀀖 , and f (􀀕) 􀀠 􀀕 .  \nKuta Software-Infinite Precalculus Evaluating Limits  \nEvaluate each limit.  \n1) 􀀖􀀎 f (x), f (x) = {􀀐xx􀀕􀀐􀀎􀀖􀀗, x 􀀐 􀀖 ,  \n􀀓  \nx  \nx  \n3)  \nlim  \nx􀁯 􀀐􀀕  \nf (x), f (x) = {􀀐􀀔􀀕x, 􀀐 􀀜 , xx 􀀟􀁴 􀀐􀀕􀀕  \nDoes not exist.  \nName  Date  Period   \n􀁤 􀀖  \n􀀡 􀀖  \n2)  \nlim  \nx􀁯 􀀖 􀀐  \n􀀖  􀀐x 􀀎 􀀖  \n􀀐x 􀀎 􀀖  \n􀀖  \n4)  \nim􀁯 􀀕 f (x), f (x) = {􀀐  􀀕􀀔,, xx 􀁤􀀡 􀀕􀀕  \n􀀐􀀖  \nEvaluate each limit. You may use the provided graph to sketch the function.  \n5)  \nxm􀀐􀀔 􀀐 f (x), f (x) = { ~~ ~~ 􀀕􀀐,  \nx 􀁤  \n􀀗 , x 􀀡  \n􀀔  \n􀀐􀀔  \n􀀐􀀔  \n6)  \nim􀁯 􀀐􀀕 f (x), f (x) = {􀀕􀀎  ,􀀎 􀀛 ,  \nx  \nx  \n􀀓  \n􀀟 􀀐􀀕  \n􀁴 􀀐􀀕  \nEvaluate each limit.  \n7)  \nim􀁯 􀀗􀀐 f (x), f (x) = {􀀘􀀎  ,  \nx 􀀟 􀀗  \nx 􀁴 􀀗  \n􀀖  \n9)  \nlim  \nx􀁯 􀀔 􀀎  \n􀀐􀀖  \nf (x), f (x) = {x􀀐􀀐􀀗 􀀘, ,  \nx 􀀟 􀀔  \nx 􀁴 􀀔  \n8)  \nlim  \nx􀁯 􀀖 􀀐  \n􀀓  \nf (x), f (x) = {x  ,􀀗x 􀀐  \n10)  \nlim  \nx􀁯 􀀐􀀖 􀀐  \n􀀐􀀔  \nf (x), f (x) = {􀀐 􀀐 􀀗x  \n􀀖 , x 􀀟 􀀖 x 􀁴 􀀖  \n􀀐 􀀗 , x 􀀟 􀀐􀀖 x 􀁴 􀀐􀀖  \nCritical thinking question:  \n11) Write a piecewise function where  \nMany answers. Ex: f (x) = {xx, 􀀐  \nx 􀀎  \nlim  \nx􀁯 􀀕 􀀐  \nf (x) 􀀠 􀀔 ,  \n􀀔 , x 􀀟 􀀕 x 􀀠 􀀕􀀔 , x 􀀡 􀀕  \nlim  \nx􀁯 􀀕 􀀎  \nf (x) 􀀠 􀀖 , and f (􀀕) 􀀠 􀀕 .  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaimj2StltcHVS","https://ap.wps.com/l/cbCaimj2StltcHVS","pdf",45120,"English","# Evaluate each limit\n## Problems 1-10\n## Critical thinking question 11","[{\"question\":\"What is the main task of the worksheet?\",\"answer\":\"Evaluate each listed limit, often involving piecewise functions and approaching specific x-values.\"},{\"question\":\"How should you handle questions that mention a graph?\",\"answer\":\"Use the provided graph to sketch the function so the limit as x approaches the given value can be determined.\"},{\"question\":\"What does the critical thinking question require?\",\"answer\":\"Write a piecewise function that satisfies specified limit behavior as x approaches a value and the function’s value at a particular input.\"}]","Evaluating Limits | PDF",1791427059]