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\nEvaluate each sum.  \nn n  \n1) 􀀶 􀀗􀀛 k 2) 􀀶 􀀔􀀙k􀀕  \nk 􀀠 􀀔 k 􀀠 􀀔  \n3) 􀀶n (􀀖􀀙k 􀀎 􀀙) 4) 􀀶n (k 􀀎 􀀕)  \nk 􀀠 􀀔 k 􀀠 􀀔  \nEvaluate each limit.  \n5)  kn 􀀔 ~~ ~~􀀔􀀕n~~􀀕~~k~~ ~~ 6)  kn 􀀔 (~~ ~~ 􀀎 kn􀀕~~􀀖 ~~)  \n7)  kn 􀀔 (~~ ~~ 􀀎 ~~ ~~􀀔~~ ~~k~~􀀖~~􀀕~~ ~~) 8)  kn 􀀔 (~~ ~~ 􀀎 ~~ ~~􀀛kn~~􀀖~~􀀕~~ ~~)  \nFor each problem, find the area under the curve over the given interval. Set up your solution using the limit as n goes to 􀁦 of the upper sum.  \n9) f (x) 􀀠 x 􀀎 􀀘; [􀀓 , 􀀜]  \n10) , 􀀖]  \nKuta Software-Infinite Precalculus  \nArea Under a Curve Using Limits of Sums  \nName  Date  Period   \nEvaluate each sum.  \nn n  \n1) 􀀶 􀀗􀀛 k 2) 􀀶 􀀔􀀙k􀀕  \nk 􀀠 􀀔 k 􀀠 􀀔  \n􀀕􀀗n 􀀕 􀀎 􀀕􀀗n ~~ ~~􀀔~~ ~~􀀙n􀀖􀀖~~ ~~ 􀀎 􀀛 n 􀀕 􀀎 ~~ ~~􀀛n􀀖  \n3) 􀀶n (􀀖􀀙k 􀀎 􀀙) 4) 􀀶n (k 􀀎 􀀕)  \nk 􀀠 􀀔 k 􀀠 􀀔  \n􀀔􀀛 n 􀀕 􀀎 􀀕􀀗n  􀀘n   n 􀀕   \n􀀎  \n􀀕 􀀕  \nEvaluate each limit.  \n5)  kn 􀀔 ~~ ~~􀀔􀀕n~~􀀕~~k~~ ~~ 6)  kn 􀀔 (~~ ~~ 􀀎 kn􀀕~~􀀖 ~~)  \n􀀙 􀀚  \n 􀀖  􀁼 􀀕􀀑􀀖􀀖􀀖  \n7)  kn 􀀔 (~~ ~~ 􀀎 ~~ ~~􀀔~~ ~~k~~􀀖~~􀀕~~ ~~) 8)  kn 􀀔 (~~ ~~ 􀀎 ~~ ~~􀀛kn~~􀀖~~􀀕~~ ~~)  \n􀀖􀀗 􀀗􀀗  \n􀁼 􀀔􀀔􀀑􀀖􀀖􀀖 􀁼 􀀔􀀗􀀑􀀙􀀙􀀚  \n􀀖 􀀖  \nFor each problem, find the area under the curve over the given interval. Set up your solution using the limit as n goes to 􀁦 of the upper sum.  \n9) f (x) 􀀠 x 􀀎 􀀘; [􀀓 , 􀀜]  \n10) , 􀀖]  \n􀀔􀀛  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaijam08PCET1L","https://ap.wps.com/l/cbCaijam08PCET1L","pdf",66495,"English","# Evaluating Finite Sums\n# Evaluating Limits\n# Finding Area Under a Curve Using Limits of Sums","[{\"question\":\"What is the primary objective of this worksheet?\",\"answer\":\"The worksheet aims to help students practice evaluating finite sums and limits, and specifically teaches how to find the area under a curve using the limit of the upper sum as n approaches infinity.\"},{\"question\":\"What mathematical concepts are covered in this document?\",\"answer\":\"The document covers sigma notation for evaluating sums, calculating limits as n approaches infinity, and the application of these limits to find the area under a curve over a given interval.\"},{\"question\":\"How are the area problems structured?\",\"answer\":\"The problems require students to set up a solution using the limit as n goes to infinity of the upper sum for a given function and a specific interval.\"}]","Area Under a Curve Using Limits of Sums - Worksheet | PDF",1791427048]