[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-523580-105":3,"doc-detail-523580-en":81,"detail-sidebar-cat-0-en-105":97},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","evaluating-limits-precalculus-worksheet-14","Evaluating Limits - Precalculus Worksheet 14","","This document provides a set of precalculus exercises focused on evaluating limits at infinity. It includes eight practice problems involving various polynomial and rational expressions where students are asked to determine the limit as the variable approaches positive or negative infinity. Additionally, a critical thinking question is included to challenge students to construct a limit function that evaluates to a specific value at infinity. This resource serves as a structured review or practice assignment for students studying calculus foundations, helping them master the behavior of functions as they grow without bound. The worksheet also features an answer key for all problems, providing immediate feedback for self-study and assessment purposes. The material is designed to facilitate a deeper understanding of limit definitions and properties in mathematical analysis.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/evaluating-limits-precalculus-worksheet-14/523580/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/evaluating-limits-precalculus-worksheet-14/523580.png","ImageObject",300,407,{"name":42,"@type":43},"MrHarris58","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",9,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the primary topic of this worksheet?","Question",{"text":63,"@type":64},"The worksheet focuses on evaluating limits of functions as x approaches positive or negative infinity.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Does this document include solutions?",{"text":68,"@type":64},"Yes, the document provides the evaluated results for each of the eight limit problems and the critical thinking example.",{"name":70,"@type":61,"acceptedAnswer":71},"What is the purpose of the critical thinking question?",{"text":72,"@type":64},"It asks students to create their own example of a function that approaches a specific value as x approaches infinity, testing their understanding of limit construction.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},523580,1791518793,{"code":4,"msg":82,"data":83},"success",{"doc_id":79,"user_id":84,"nickname":42,"user_avatar":85,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":86,"file_id":87,"file_url":88,"file_type":89,"file_size":90,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":26,"language":91,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":92,"faqs":93,"seo_title":94,"seo_description":12,"update_tm":95,"read_time":96,"preview_page_count":4},687212988360,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Kuta Software-Infinite Precalculus Evaluating Limits  \nEvaluate each limit.  \n1) lim  x 􀀐 􀀖  x􀁯 􀁦 􀀕x 􀀕 􀀎 􀀕x 􀀎 􀀔  \n3) lim ~~ ~~x~~ ~~x􀁯 􀁦 x 􀀎 􀀖  \n5) lim (x 􀀖 􀀎 x􀀕 􀀐 x) x􀁯 􀁦  \n7) lim (x 􀀗 􀀎 x􀀖 􀀐 􀀕x 􀀕 􀀐 􀀔) x􀁯 􀁦  \nName  Date  Period   \n2) lim (x 􀀖 􀀐 􀀖 x 􀀎 􀀕)  \nx􀁯 􀀐􀁦  \nx 􀀖  \n4)  􀀕x 􀀕 􀀐 􀀕   \n6) lim (x 􀀘 􀀐 􀀖 x 􀀖 􀀎 􀀖 x 􀀐 􀀔) x􀁯 􀁦  \n8)  x~~ ~~􀀕􀀐x􀀎~~ ~~􀀎x~~ ~~~~ ~~􀀔~~ ~~  \nCritical thinking question:  \n9) Give an example of a limit that goes to 􀀗 as x goes to 􀁦 .  \nKuta Software-Infinite Precalculus Evaluating Limits  \nEvaluate each limit.  \n1) lim  x 􀀐 􀀖  x􀁯 􀁦 􀀕x 􀀕 􀀎 􀀕x 􀀎 􀀔  \n􀀓  \n3) lim ~~ ~~x~~ ~~x􀁯 􀁦 x 􀀎 􀀖  \n􀀔  \n5) lim (x 􀀖 􀀎 x􀀕 􀀐 x) x􀁯 􀁦  \n􀁦  \n7) lim (x 􀀗 􀀎 x􀀖 􀀐 􀀕x 􀀕 􀀐 􀀔) x􀁯 􀁦  \n􀁦  \nName  Date  Period   \n2) lim (x 􀀖 􀀐 􀀖 x 􀀎 􀀕)  \nx􀁯 􀀐􀁦  \n􀀐􀁦  \n􀀖  \n4)  􀀕xx~~􀀕 ~~􀀐~~ ~~􀀕  \n􀁦  \n6) lim (x 􀀘 􀀐 􀀖 x 􀀖 􀀎 􀀖 x 􀀐 􀀔) x􀁯 􀁦  \n􀁦  \n8)  x~~ ~~􀀕􀀐x􀀎~~ ~~􀀎x~~ ~~~~ ~~􀀔~~ ~~  \n􀀓  \nCritical thinking question:  \n9) Give an example of a limit that goes to 􀀗 as x goes to 􀁦 .  \n 􀀗x   \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)","cbCaiaNDq0z39UMx","https://ap.wps.com/l/cbCaiaNDq0z39UMx","pdf",33202,"English","# Evaluating Limits at Infinity\n## Practice Problems\n## Critical Thinking Question","[{\"question\":\"What is the primary topic of this worksheet?\",\"answer\":\"The worksheet focuses on evaluating limits of functions as x approaches positive or negative infinity.\"},{\"question\":\"Does this document include solutions?\",\"answer\":\"Yes, the document provides the evaluated results for each of the eight limit problems and the critical thinking example.\"},{\"question\":\"What is the purpose of the critical thinking question?\",\"answer\":\"It asks students to create their own example of a function that approaches a specific value as x approaches infinity, testing their understanding of limit construction.\"}]","Evaluating Limits - Precalculus Worksheet 14 | PDF",1791427057,5,{"code":4,"msg":82,"data":98},[99,103,107,110,114,119,124,129,133,136,140],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":104,"show_sort_weight":105,"slug":106},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":108,"slug":109},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},"Comic",60,"comic",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},6,"Technology",50,"technology",{"id":120,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":122,"slug":123},7,"Healthcare",40,"healthcare",{"id":125,"doc_module":4,"doc_module_name":25,"category_name":126,"show_sort_weight":127,"slug":128},8,"Research & Report",30,"research-report",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":130,"show_sort_weight":131,"slug":132},"Religion & Spirituality",20,"religion-spirituality",{"id":131,"doc_module":4,"doc_module_name":25,"category_name":134,"show_sort_weight":131,"slug":135},"World Cup","world-cup",{"id":137,"doc_module":4,"doc_module_name":25,"category_name":138,"show_sort_weight":137,"slug":139},10,"Lifestyle","lifestyle",{"id":141,"doc_module":4,"doc_module_name":25,"category_name":142,"show_sort_weight":96,"slug":143},19,"General","general"]