MAT 125A Homework 3M.FukudaPlease submit your answers at the discussion session on October 25th Thursday.You can use theorems in the lecuture unless otherwise stated. When you do so write thosestatements clearly instead of quoting them by numbers.1. Lets,t∈Randf1,f2: (s,t)→R.Takea∈(s,t) and, suppose limx→a-f1(x) andlimx→a-f2(x) exist. LetLi= limx→a-fi(x) fori= 1,2.1) SupposeL1,L2∈R. Then, show thatL= limx→a-f1(x)+f2(x) exits andL=L1+L2.2) SupposeL1∈RandL2=∞. Then, does the limitL= limx→a-f1(x) +f2(x) exist?Prove your idea.3) SupposeL1=-∞andL2=∞. Then, does the limitL= limx→a-f1(x)+f2(x) exist?Explain your idea briefly.2. Find the redious of convergence and determine the exact interval of convergence.
This is the end of the preview.
access the rest of the document.