hi all,(adsbygoogle = window.adsbygoogle || []).push({});

like many here i have also picked up the spivak calculus text and run into some problems.

i am reading the fifth chapter which introduces 'limits' and i can't get my head around the idea of using minimum (the concept was introduced in the problems of the first chapter and it reappears in chapter 5 without any formal discussion about it). i haven't figured out how to approach it yet. i guess thats what i mean to ask here. i don't think i am making any sense. probably an example will help. this is from the book, towards the end of the chapter, consider:

f(x) = x^2 + x, and x approaches a,

according to the definition in the book, we have to find a [tex]\delta[/tex] > 0 such that |x^2 + x - (a^2 + a)| < [tex]\epsilon[/tex]

it then breaks down the function into x^2 and x, so that we need 2 [tex]\delta[/tex]s

one for the x^2 and the other for x,

if 0 < |x - a| < [tex]\delta[/tex]1, then |x^2 - a^2| < [tex]\epsilon[/tex]/2

if 0 < |x - a| < [tex]\delta[/tex]2, then |x - a| < [tex]\epsilon[/tex]/2

now, for some reason i don't know,

[tex]\delta[/tex]1 = min (1, [tex]\epsilon[/tex]/2/2|a| + 1)

[tex]\delta[/tex]2 = [tex]\epsilon[/tex]/2

what is going on here?

this is a very confusing first post and i am very sorry about it. (imagine the confusion in my head perhaps i can try to clarify my question after a few responses. thanks in advance!

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# Limits and minimum

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