[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523579-105":59,"doc-detail-523579-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","evaluating-limits-worksheet","Evaluating Limits - Worksheet","","This document is a precalculus educational worksheet focused on evaluating limits, specifically those involving essential discontinuities. It provides a set of six mathematical exercises requiring students to determine the existence and values of limits as the variable x approaches various constants, including scenarios resulting in positive or negative infinity or limits that do not exist. Additionally, it features a critical thinking question prompting the construction of a right-sided limit example. Designed for instructional use, the worksheet serves as a practical assessment tool for students to master algebraic limit evaluation techniques.",{"@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/evaluating-limits-worksheet/523579/",{"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-worksheet/523579.png","ImageObject",300,407,{"name":92,"@type":93},"MrHarris58","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What are the primary topics covered in this worksheet?","Question",{"text":112,"@type":113},"The worksheet focuses on evaluating limits, particularly those related to essential discontinuities in functions.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What types of outcomes are expected when evaluating the provided limit exercises?",{"text":117,"@type":113},"The exercises challenge students to identify if a limit exists, if it diverges to positive or negative infinity, or if it does not exist.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the goal of the critical thinking question?",{"text":121,"@type":113},"The critical thinking question asks the student to demonstrate their understanding of limits by constructing a specific example of a right-sided limit that approaches infinity as x approaches 2.","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},523579,1791519120,{"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":44,"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":143,"read_time":24,"preview_page_count":4},687212988360,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Kuta Software-Infinite Precalculus Evaluating Limits  \nEvaluate each limit.  \n1)  \nim􀁯 􀀗  \n􀀕  \nx  \n􀀗x 􀀐 􀀔􀀙  \n3)  \nlim  \nx􀁯 􀀕 􀀐  \n􀀕  \n􀀐  \nx 􀀐 􀀕  \n5)  \nlim  \nx􀁯 􀀐􀀖  \n􀀕x  \n􀀐  \nx 􀀎 􀀖  \nName  Date  Period   \n2)  \nlim  \nx􀁯 􀀐􀀔  \nx 􀀎 􀀘  \nx 􀀕 􀀎 􀀕x 􀀎 􀀔  \n4)  \nlim  \nx􀁯 􀀐􀀗 􀀎  \nx 􀀎 􀀕  \nx 􀀕 􀀎 􀀛 x 􀀎 􀀔􀀙  \n6)  \nlim  \nx􀁯 􀀘  \nx 􀀐 􀀕  \nx 􀀕 􀀐 􀀔􀀓x 􀀎 􀀕􀀘  \nCritical thinking question:  \n7) Give an example of a right-sided limit that goes to 􀁦 as x goes to 2.  \nKuta Software-Infinite Precalculus Evaluating Limits  \nEvaluate each limit.  \n1)  \nim􀁯 􀀗  \n􀀕  \nx  \n􀀗x 􀀐 􀀔􀀙  \nDoes not exist.  \n3)  \nlim  \nx􀁯 􀀕 􀀐  \n􀀕  \n􀀐  \nx 􀀐 􀀕  \n􀁦  \n5)  \nlim  \nx􀁯 􀀐􀀖  \n􀀕x  \n􀀐  \nx 􀀎 􀀖  \nDoes not exist.  \nName  Date  Period   \n2)  \nlim  \nx􀁯 􀀐􀀔  \nx 􀀎 􀀘  \nx 􀀕 􀀎 􀀕x 􀀎 􀀔  \n4)  \n􀁦  \nxm􀀐􀀗􀀎  \nx 􀀎 􀀕  \nx 􀀕 􀀎 􀀛 x 􀀎 􀀔􀀙  \n􀀐􀁦  \n6)  \nlim  \nx􀁯 􀀘  \nx 􀀐 􀀕  \nx 􀀕 􀀐 􀀔􀀓x 􀀎 􀀕􀀘  \n􀁦  \nCritical thinking question:  \n7) Give an example of a right-sided limit that goes to 􀁦 as x goes to 2.  \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)","cbCaikvGnnQ04Mby","https://ap.wps.com/l/cbCaikvGnnQ04Mby","pdf",51334,"English","# Exercises\n## Critical Thinking Question","[{\"question\":\"What are the primary topics covered in this worksheet?\",\"answer\":\"The worksheet focuses on evaluating limits, particularly those related to essential discontinuities in functions.\"},{\"question\":\"What types of outcomes are expected when evaluating the provided limit exercises?\",\"answer\":\"The exercises challenge students to identify if a limit exists, if it diverges to positive or negative infinity, or if it does not exist.\"},{\"question\":\"What is the goal of the critical thinking question?\",\"answer\":\"The critical thinking question asks the student to demonstrate their understanding of limits by constructing a specific example of a right-sided limit that approaches infinity as x approaches 2.\"}]","Evaluating Limits - Worksheet | PDF",1791427055]