[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523571-105":59,"doc-detail-523571-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","infinite-precalculus-power-series-worksheet","Infinite Precalculus Power Series - Worksheet","","Worksheet for Infinite Precalculus focusing on power series approximation and complex-number forms. Problems instruct students to use the fifth partial sum of the exponential series to approximate given values and round to the nearest thousandth. Additional exercises use the fifth partial sum for sine and cosine approximations, determine power series representations g(x) from xn/n and specify convergence intervals, and then write expressions in exponential and rectangular forms. Complex logarithms and exponential equations are included, followed by critical thinking evaluation questions.",{"@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/infinite-precalculus-power-series-worksheet/523571/",{"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/infinite-precalculus-power-series-worksheet/523571.png","ImageObject",300,407,{"name":92,"@type":93},"pixelkiddo","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How are values approximated using the exponential series in this worksheet?","Question",{"text":112,"@type":113},"Use the fifth partial sum of the exponential series and round each result to the nearest thousandth.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is required when finding a power series representation of g(x)?",{"text":117,"@type":113},"Use the given xn/n pattern to form the power series for g(x) and indicate the interval where the series converges.",{"name":119,"@type":110,"acceptedAnswer":120},"What types of complex-number tasks appear after the power series sections?",{"text":121,"@type":113},"Students convert expressions to exponential and rectangular forms, evaluate selected expressions, and solve equations over the complex numbers.","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},523571,1791518963,{"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":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"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":52,"preview_page_count":4},962090883892,"https://ap-avatar.wpscdn.com/avatar/e00115db34f3e0f11b?x-image-process=image/resize,m_fixed,w_180,h_180&k=1790152879550218658","Kuta Software-Infinite Precalculus Power Series  \nName  Date  Period   \nUse the fifth partial sum of the exponential series to approximate each value. Round your answer to the nearest thousandth.  \n1) e 􀀓􀀑􀀗 2) e 􀀐􀀓􀀑􀀘  \nUse the fifth partial sum of the power series for sine or cosine to approximate each value. Round your answer to the nearest thousandth.  \n3) sin ~~ ~~􀀘􀁓􀀚~~ ~~ 4) sin ~~ ~~􀀚􀀔~~ ~~  \nUse  xn 􀀠  􀀔  to find a power series representation of g(x). Indicate the interval in which n 􀀠 􀀓 􀀔 􀀐 x  \nthe series converges.  \n5) g(x) 􀀠 ~~ ~~􀀔~~ ~~~~ ~~x~~ 􀀕 ~~ 6) g(x) 􀀠 ~~ ~~􀀖~~ ~~􀀎􀀗􀀕x~~ 􀀕 ~~  \n7) g(x) 􀀠 ~~ ~~􀀔~~ ~~~~ ~~x~~ 􀀕 ~~ 8) g(x) 􀀠 ~~ ~~􀀖~~ ~~~~ ~~x~~ 􀀕 ~~  \nUse  xn 􀀠  􀀔  to find a power series representation of g(x). Indicate the interval in which n 􀀠 􀀓 􀀔 􀀐 x  \nthe series converges. Then graph g(x) and the sixth partial sum ofits power series.  \n9) g(x) 􀀠 􀀕~~ ~~x~~ 􀀕 ~~  \n10) g(x) 􀀠 ~~ ~~􀀔~~ ~~~~ ~~x~~ 􀀕 ~~  \nWrite each in exponential form.  \n11) 􀀐i 􀀔􀀚 12) 􀀕 􀀕 􀀐 􀀕 i 􀀕  \n13) 􀀐􀀖 􀀐 􀀖 i 􀀖 14) 􀀐 􀀖 􀀎 i  \nWrite each in rectangular form.  \n 􀀔􀀔 i􀁓   􀀗i􀁓   \n15) 􀀙 e 􀀙 16) 􀀗 e 􀀖  \n i􀁓   􀀘i􀁓   \n17) 􀀗 e 􀀖 18) 􀀙 e 􀀖  \nWrite each as a complex number in rectangular form.  \n19) ln 􀀐􀀙􀀑􀀚 20) ln 􀀐􀀘  \n21) ln 􀀐􀀔􀀖 22) ln 􀀐􀀖  \nSolve each equation over the complex numbers.  \n23) ez 􀀎 􀀔􀀓 􀀠 􀀔 24) 􀀖 􀀠 ez 􀀎 􀀔􀀓  \n25) e 􀀕z 􀀎 􀀙 􀀠 􀀐􀀔 26) 􀀕􀀓 ez 􀀎 􀀔􀀓􀀓 􀀠 􀀐e 􀀕z  \nCritical thinking questions:  \n27) Evaluate: i 􀀕i 28) Evaluate: ln i  \nKuta Software-Infinite Precalculus Power Series  \nName  Date  Period   \nUse the fifth partial sum of the exponential series to approximate each value. Round your answer to the nearest thousandth.  \n1) e 􀀓􀀑􀀗 􀀔􀀑􀀗􀀜􀀕 2) e 􀀐􀀓􀀑􀀘 􀀓􀀑􀀙􀀓􀀚  \nUse the fifth partial sum of the power series for sine or cosine to approximate each value. Round your answer to the nearest thousandth.  \n3) sin ~~ ~~􀀘􀁓􀀚~~ ~~ 􀀓􀀑􀀚􀀛􀀕 4) sin ~~ ~~􀀚􀀔~~ ~~ 􀀓􀀑􀀜􀀙􀀙  \nUse  xn 􀀠  􀀔  to find a power series representation of g(x). Indicate the interval in which n 􀀠 􀀓 􀀔 􀀐 x  \nthe series converges.  \n5) g(x) 􀀠 ~~ ~~􀀔~~ ~~~~ ~~x~~ 􀀕~~ n (~~ ~~􀀕~~ ~~~~ ~~x~~ ~~􀀕~~ ~~) n 6) g(x) 􀀠 ~~ ~~􀀖~~ ~~􀀎􀀗􀀕x~~ 􀀕 ~~  (~~ ~~􀀔~~ ~~􀀐􀀗􀀕x~~ ~~􀀕~~ ~~) n Converges in: (􀀐􀀔 , 􀀔) nConverges in: ( 􀀐 ~~ ~~􀀔􀀓􀀕~~ ~~, ~~ ~~􀀔􀀓􀀕~~ ~~)  \n7) g(x) 􀀠 ~~ ~~􀀔~~ ~~~~ ~~x~~ 􀀕~~ n (x 􀀕 )n 8) g(x) 􀀠 ~~ ~~􀀖~~ ~~~~ ~~x~~ 􀀕~~ n (~~ ~~􀀕~~ ~~) n  \nConverges in: (􀀐􀀔 , 􀀔) Converges in: ( 􀀐 􀀖 , 􀀖 )  \nUse  xn 􀀠  􀀔  to find a power series representation of g(x). Indicate the interval in which n 􀀠 􀀓 􀀔 􀀐 x  \nthe series converges. Then graph g(x) and the sixth partial sum ofits power series.  \n9) g(x) 􀀠 􀀕~~ ~~x~~ 􀀕 ~~  \nn ( 􀀐 ~~ ~~x􀀕􀀕~~ ~~) n  \nConverges in: ( 􀀐 􀀕 , 􀀕 )  \n10) g(x) 􀀠 ~~ ~~􀀔~~ ~~~~ ~~x~~ 􀀕 ~~  \n(x 􀀕 )n  \n􀀓onverges in: (􀀐􀀔 , 􀀔)  \nWrite each in exponential form.  \n11) 􀀐i 􀀔􀀚 12) 􀀕 􀀕 􀀐 􀀕 i 􀀕  \n 􀀖 i􀁓   􀀚i􀁓 􀀔􀀚 e 􀀕 􀀗 e 􀀗  \n13) 􀀐􀀖 􀀐 􀀖 i 􀀖 14) 􀀐 􀀖 􀀎 i  \n􀀗i􀁓   􀀘i􀁓   \n􀀙 e 􀀖 􀀕 e 􀀙  \nWrite each in rectangular form.  \n 􀀔􀀔 i􀁓   􀀗i􀁓   \n15) 􀀙 e 􀀙 16) 􀀗 e 􀀖  \n􀀖 􀀖 􀀐 􀀖 i 􀀐􀀕 􀀐 􀀕 i 􀀖  \n i􀁓   􀀘i􀁓   \n17) 􀀗 e 􀀖 18) 􀀙 e 􀀖  \n􀀕 􀀎 􀀕 i 􀀖 􀀖 􀀐 􀀖 i 􀀖   \nWrite each as a complex number in rectangular form.  \n19) ln 􀀐􀀙􀀑􀀚 20) ln 􀀐􀀘  \n􀀔􀀑􀀜􀀓􀀕 􀀎 i􀁓 􀀔􀀑􀀙􀀓􀀜 􀀎 i􀁓  \n21) ln 􀀐􀀔􀀖 22) ln 􀀐􀀖  \n􀀕􀀑􀀘􀀙􀀘 􀀎 i􀁓 􀀔􀀑􀀓􀀜􀀜 􀀎 i􀁓  \nSolve each equation over the complex numbers.  \n23) ez 􀀎 􀀔􀀓 􀀠 􀀔 24) 􀀖 􀀠 ez 􀀎 􀀔􀀓  \n􀁞ln 􀀜 􀀎 i􀁓 􀀎 􀀕 i􀁓n􀁠 􀁞ln 􀀚 􀀎 i􀁓 􀀎 􀀕 i􀁓n􀁠  \n25) e 􀀕z 􀀎 􀀙 􀀠 􀀐􀀔 26) 􀀕􀀓 ez 􀀎 􀀔􀀓􀀓 􀀠 􀀐e 􀀕z  \n􀁞 ~~ ~~ln~~ ~~􀀚~~ ~~􀀎~~ ~~i~~ ~~􀀎~~ ~~􀀕~~ ~~i􀁓n~~ ~~ 􀁠 􀁞ln 􀀔􀀓 􀀎 i􀁓 􀀎 􀀕 i􀁓n􀁠  \nCritical thinking questions:  \n27) Evaluate: i 􀀕i 28) Evaluate: ln i ~~ ~~i 􀀐􀁓  \ne  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaipF213fD9SwX","https://ap.wps.com/l/cbCaipF213fD9SwX","pdf",41494,"English","# Use partial sums for approximations\n## Exponential series approximations\n## Sine and cosine approximations\n# Power series representation and convergence\n## Represent g(x) using xn/n\n## Indicate the interval of convergence\n## Graph g(x) and a partial sum\n# Convert forms for complex expressions\n## Exponential form\n## Rectangular form\n# Solve and evaluate over complex numbers\n## Solve exponential equations\n## Critical thinking evaluations","[{\"question\":\"How are values approximated using the exponential series in this worksheet?\",\"answer\":\"Use the fifth partial sum of the exponential series and round each result to the nearest thousandth.\"},{\"question\":\"What is required when finding a power series representation of g(x)?\",\"answer\":\"Use the given xn/n pattern to form the power series for g(x) and indicate the interval where the series converges.\"},{\"question\":\"What types of complex-number tasks appear after the power series sections?\",\"answer\":\"Students convert expressions to exponential and rectangular forms, evaluate selected expressions, and solve equations over the complex numbers.\"}]","Infinite Precalculus Power Series - Worksheet | PDF",1791427037]