[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522809-105":59,"doc-detail-522809-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-1","Evaluating Limits - Worksheet 1","","This educational resource from Kuta Software provides a structured worksheet for students to practice evaluating limits in calculus. The document contains a series of ten practice problems involving constant, linear, polynomial, rational, and trigonometric functions, followed by two critical thinking questions that challenge students to construct examples of limits with specific output values. Each problem is designed to test the application of limit laws and direct evaluation techniques. This material serves as a supplementary assessment tool for calculus curriculum and independent study.",{"@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-1/522809/",{"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-1/522809.png","ImageObject",300,407,{"name":92,"@type":93},"Alex Sinclair","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","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},"How do you evaluate a limit using direct substitution?","Question",{"text":112,"@type":113},"You replace the variable x with the constant value that x is approaching in the limit expression, assuming the function is defined at that point.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is an example of a limit that evaluates to 4?",{"text":117,"@type":113},"One common example is the limit of x as x approaches 4, written as lim x (x→4) = 4.",{"name":119,"@type":110,"acceptedAnswer":120},"What is an example of a quadratic function limit that evaluates to 9?",{"text":121,"@type":113},"An example is the limit of x squared as x approaches 3, written as lim x^2 (x→3) = 9.","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},522809,1791549770,{"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},1099523882182,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Kuta Software-Infinite Calculus Name___________________________________  \nEvaluating Limits Date________________ Period____  \nEvaluate each limit.  \n1) lim 5 2) lim (−x + 2)  \nx→ −1 5  \nx→ − ~~ ~~  \n2  \n3)  (x 3 − x 2 − 4) 4) 1 (− ~~ ~~x22~~ ~~ + 2x + 4)  \n5) lim − x + 3 6) lim − 2x + 4  \nx→ 3 3  \nx→ ~~ ~~  \n2  \n7) lim − ~~ ~~2~~ ~~x~~ ~~−~~ ~~4~~ ~~ 8) lim  −x − 3  x→ 1 x − 6x + 8 x→ ~~ ~~32 x 2 + x + 1  \n9) lim sin (x) 10) lim 2cos (x)  \nx→ π 3π  \nx→ ~~ ~~  \n4  \nCritical thinking questions:  \n11) Give an example of a limit that evaluates to 4. 12) Give an example of a limit of a quadratic  \nfunction where the limit evaluates to 9.  \nKuta Software-Infinite Calculus Name   \nEvaluating Limits Date  Period   \nEvaluate each limit.  \n1) lim 5  \nx→ −1  \n5  \n3) lim (x 3 − x 2 − 4) x→ 2  \n0  \n5) lim − x + 3 x→ 3  \n− 6  \n7) lim − ~~ ~~2~~ ~~x~~ ~~−~~ ~~4~~  ~~x→ 1 x − 6x + 8  \n1  \n9) lim sin (x)  \nx→ π  \n0  \n2) lim  (−x + 2)  \n5  \nx→ −  \n2  \n9  \n2  \n4) 1 (− ~~ ~~x22~~ ~~ + 2x + 4) 11  \n2  \n6) lim − 2x + 4  \n3  \nx→ ~~ ~~  \n2  \n− 7  \n8) lim  −x − 3  x→ ~~ ~~32 x 2 + x + 1  \n 18  \n−  \n19  \n10) lim  \n3π  \nx→ ~~  ~~4  \n2cos (x)  \n− 2  \nCritical thinking questions:  \n11) Give an example of a limit that evaluates to 4.  \nMany answers. Ex: lim x  \nx→ 4  \n12) Give an example of a limit of a quadratic function where the limit evaluates to 9.  \nMany answers. Ex: lim x 2  \nx→ 3  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaiaBEE8x5Hscx","https://ap.wps.com/l/cbCaiaBEE8x5Hscx","pdf",25654,"English","# Practice Problems\n## Direct Evaluation\n## Critical Thinking Questions","[{\"question\":\"How do you evaluate a limit using direct substitution?\",\"answer\":\"You replace the variable x with the constant value that x is approaching in the limit expression, assuming the function is defined at that point.\"},{\"question\":\"What is an example of a limit that evaluates to 4?\",\"answer\":\"One common example is the limit of x as x approaches 4, written as lim x (x→4) = 4.\"},{\"question\":\"What is an example of a quadratic function limit that evaluates to 9?\",\"answer\":\"An example is the limit of x squared as x approaches 3, written as lim x^2 (x→3) = 9.\"}]","Evaluating Limits - Worksheet 1 | PDF",1791426194]