I will introduce the epsilonN definition of a limit and will also show you how to write a rigorous proof for a limit as x goes to infinity. I will help you understand the definition by using a specific epsilon value, graphs of the function, and the line y=Lepsilon, and solving for a corresponding N. And remember "given, choose, suppose, and check".
#calculus #math #maths #college #blackpenredpen

This is similar to the epsilondelta proofs for limits and you can check out that introduction here:    • epsilondelta definition ultimate int...  

0:00 I will help you understand the εN definition for a finite limit at infinity
0:19 the 4 main cases of a rigorous definition of a limit
2:24 the εN definition
4:14 how to easily write a rigorous limit proof
11:32 an actual example with ε=0.02 and find a N

#calculus #blackpenredpen #realanalysis #math #college

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