We appreciate your visit to Suppose tex f D to mathbb R tex with tex x 0 tex an accumulation point of tex D tex Assume tex L 1 tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
L1 and L2 are limits of f at xo, thus |L1-L2|<ε implies L1 = L2 by the definition of limit.
If L1 and L2 are limits of f at xo, then for every ε > 0, there exist δ1, δ2 > 0 such that 0 < | x - xo | < δ1, and 0 < | x - xo | < δ2 implies | f(x) - L1 | < ε/2 and | f(x) - L2 | < ε/2, respectively.
Therefore, for any ε > 0, there is a δ = min
{δ1, δ2} > 0, such that 0 < | x - xo | < δ implies | f(x) - L1 | < ε/2 and | f(x) - L2 | < ε/2.
Thus, | L1 - L2 | ≤ | L1 - f(x) | + | f(x) - L2 | < ε/2 + ε/2 = ε.
Since ε can be made arbitrarily small, it follows that L1 = L2.
L1 and L2 are limits of f at xo, thus |L1-L2|<ε implies L1 = L2 by the definition of limit.
learn more about limits here
https://brainly.com/question/30339394
#SPJ11
Thanks for taking the time to read Suppose tex f D to mathbb R tex with tex x 0 tex an accumulation point of tex D tex Assume tex L 1 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
