Calculus proof help please
I really need help on this one proof and I've already attempted it but I'm no sure if it makes any sense!
Here are a couple of this to remember to understand what I'll type...
abs() = absolute value of something
x->a = x approaches a
e = epsilon
d = delta
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Here's the problem
If lim f(x) = L as x->a, where L<0, then there exist N(a, e) such that f(x)<0 for every x in N(a,e)
Prove that the statement above is true
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My Attempt
Nothing...I'm stumped...I don't even know how to start this other than...
Let e > 0 and d > 0
That means abs(f(x) - L) < e and abs(x-a) < e
I guess...substitute L with (-L) so, that will make it abs(f(x) + L) < e?
Then I'm stuck after that...I'm not even sure if what I did was right
11 Comments • Newest first
Is the question asked EXACTLY like that? If lim f(x) = L as x->a, where L<0, then there exist N(a, e) such that f(x)<0 for every x in N(a,e)
And I don't get it... You should have e > 0 be given, find d > 0 such that 0 < abs(x-a) < d, then abs(f(x) - L) < e. Then... I dunno the rest cus i took this 2 years ago :c
I'm always on vacation mode with or without maple or school
[quote=voyance] but if I'm extremely bored, I try to draw a perfect Ilbi lol[/quote]
Something like that sounds familiar on my first day of BC calc, but then again, it was the first day...I was still on vacation mode.
[quote=Schokoshake]Exactly...what are you proving?
Thank you...[/quote]
To be honest, I am just going by what my professor wrote on this piece of paper that he photocopied for my class. I guess he wants me to find the condition or the x in N(a,e) so that f(x) < 0? I don't really know
'
@oyster: I don't know what these proofs lead to but I know I can't use anything else other than limits (which includes epsilon-delta proofs) and it's properties and basic algebra. I doodle in class when I'm bored...but if I'm extremely bored, I try to draw a perfect Ilbi lol
@voyance: No, by "sleeping" I mean daydreaming
Wait a minute...is this like the very first lecture on limit proves for derivatives o.o
Exactly...what are you proving?
Thank you...
@oyster: WHY? WHY DID YOU SLEEP? I'd bet 1 Windian Meso that you weren't even sleepy when you slept! </3
@Schokoshake: Re-read the problem...and find a way to prove that conclusion. It's a proof, not a generic problem. (Not trying to be offensive or trying to make you feel/look stupid when I wrote "re-read the problem". I guess, I'll edit my original post
You stated the problem but it's not asking for anything. :l
As soon as I saw the words "e = epsilon, d = delta" I thought of the dirac delta functions...
I think this looks like Calc 1 or beginning Calc to me...
I fell alseep on all the proofs, I only know how to take derivates/integrals
Calc 1? just basic calculus I'd assume...
is this calc bc or calc 3?