[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522850-105":59,"doc-detail-522850-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","differentials-worksheet-04-differentials","Differentials - Worksheet 04 - Differentials","","Infinite Calculus differentials worksheet covering multiple types of problems. Students compute the differential dy for given functions, derive general expressions for both dy and Δy, and evaluate dy and Δy at a specified x0 with dx = Δx. The sheet also includes linear approximation tasks using differential-based estimates, and uncertainty propagation problems for a sphere’s volume and a square’s area. The problems guide sketching of dx, Δx, dy, and Δy using a provided graph.",{"@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/differentials-worksheet-04-differentials/522850/",{"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/differentials-worksheet-04-differentials/522850.png","ImageObject",300,407,{"name":92,"@type":93},"Quinn Holloway","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-14","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do I find dy for a given function on this worksheet?","Question",{"text":112,"@type":113},"Differentiate the function with respect to x and multiply by dx to express dy in terms of x and dx.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the relationship between dx and Δx in these problems?",{"text":117,"@type":113},"The worksheet states dx = Δx, so the computed differential can be used as an approximation for the change Δy when applying linearization.",{"name":119,"@type":110,"acceptedAnswer":120},"How is propagated error estimated for the volume of a sphere and the area of a square?",{"text":121,"@type":113},"Use the differential formulas dV and dA derived from V = (4/3)πr^3 and A = s^2, then substitute the given measured values and the possible errors dr or ds to approximate ΔV and ΔA.","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},522850,1791490291,{"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":29,"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},2336474466712,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Kuta Software-Infinite Calculus Name___________________________________  \nDifferentials Date________________ Period____  \nFor each problem, find the differential dy.  \n1) y = −x3 − 2 3  \n2) y = −  x  \nFor each problem, find the general formulas for dy and ∆y.  \n3) y = −x3 − 2 2  \n4) y =  x  \nFor each problem, find dy and ∆y, given x0 and dx = ∆x. You may use the provided graph of the function to sketch dx, ∆x, dy, and ∆y.  \n5) y = 2x~~ ~~ ; x0 = −5, dx = ∆x = 52  \n6) y = −x3 + 1; x0 = −1, dx = ∆x = − ~~ ~~12  \n−2 −1.5 −1 −0.5 x  \nFor each problem, find a linear approximation of the given quantity.  \n7) sin 122° 8) 6.994  \nUse differentials to solve each problem.  \n9) The radius of a sphere is measured to be 7 cm, with a possible error of ±~~ ~~110 cm. Estimate the possible propagated error in the calculated volume.  \n10) The sides of a square are measured to be 4 in, with a possible error of ±15 in. Estimate the possible propagated error in the calculated area.  \nKuta Software-Infinite Calculus Name___________________________________  \nDifferentials Date________________ Period____  \nFor each problem, find the differential dy.  \n1) y = −x3 − 2 3  \n2) y = − ~~ ~~  \ndy = −3x2 dx x  \ndy =  3 dx  \nx 2  \nFor each problem, find the general formulas for dy and ∆y.  \n3) y = −x3 − 2 2  \n4) y = ~~ ~~  \ndy = −3x2 dx x  \n∆y = −3x2 ∆x − 3x(∆x)2 − (∆x)3  2   \ndy = − dx  \nx2  \n∆y = − ~~ ~~x2~~ ~~∆xx∆x~~ ~~  \nFor each problem, find dy and ∆y, given x0 and dx = ∆x. You may use the provided graph of the function to sketch dx, ∆x, dy, and ∆y.  \n5) y = 2x~~ ~~ ; x0 = −5, dx = ∆x = 52  \ndy = − ~~ ~~15 = −0.2 ∆y = − ~~ ~~25 = −0.4  \nFor each problem, find a linear approximation of the given quantity.  \n7) sin 122° 8) 6.994  \nf (x) = sin x, f ' (x) = cos x  \nx0 = ~~ ~~2π3~~ ~~ radians, ∆x = ~~ ~~π90 radians  \nf (x0 + ∆x ) ≈ f (x0) + f ' (x0)∆x = ~~ ~~90~~ ~~1380−~~ ~~π ≈ 0.8486  \nf (x) = x4 , f ' (x) = 4x3  \nx0 = 7, ∆x = −0.01  \nf (x0 + ∆x ) ≈ f (x0) + f ' (x0)∆x = ~~ ~~5968252 = 2387.28  \nUse differentials to solve each problem.  \n9) The radius of a sphere is measured to be 7 cm, with a possible error of ±~~ ~~110 cm. Estimate the possible propagated error in the calculated volume.  \nV = 43πr3 , dV = 4πr2 dr  \nr = 7, dr = ±0.1  \n∆V ≈ dV = ±~~ ~~985π~~ ~~ ≈ ±61.5752 cm³  \n10) The sides of a square are measured to be 4 in, with a possible error of ±15 in. Estimate the possible propagated error in the calculated area.  \n2  \nA = s , dA = 2s ds  \ns = 4, ds = ±0.2  \n∆A ≈ dA = ±~~ ~~85 = ±1.6 in²  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCait91fOse7Znl","https://ap.wps.com/l/cbCait91fOse7Znl","pdf",45333,"English","# Find the differential dy\n# Derive general formulas for dy and Δy\n# Compute dy and Δy using x0 and dx = Δx\n# Linear approximations using differentials\n# Use differentials for uncertainty/propagated error","[{\"question\":\"How do I find dy for a given function on this worksheet?\",\"answer\":\"Differentiate the function with respect to x and multiply by dx to express dy in terms of x and dx.\"},{\"question\":\"What is the relationship between dx and Δx in these problems?\",\"answer\":\"The worksheet states dx = Δx, so the computed differential can be used as an approximation for the change Δy when applying linearization.\"},{\"question\":\"How is propagated error estimated for the volume of a sphere and the area of a square?\",\"answer\":\"Use the differential formulas dV and dA derived from V = (4/3)πr^3 and A = s^2, then substitute the given measured values and the possible errors dr or ds to approximate ΔV and ΔA.\"}]","Differentials - Worksheet 04 - Differentials | PDF",1791426235]