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Analysis class- calling smart people (stay out 609)

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said_aouita's avatar

said_aouita

Banned

8,532 posts
Jan 21, 2011 7:06 AM
This is not my homework. I'm not smart enough to solve these types of problems, just helping someone out and thought I'd ask all the smart people on Ohio Chatter.

Does this make sense to you?


lim as x->0 of f'(x) where f(x) = e^(-1/x^2) = 0
Jan 21, 2011 7:06am
september63's avatar

september63

Senior Member

5,789 posts
Jan 21, 2011 8:40 AM
What you talkin bout, Willis?
Jan 21, 2011 8:40am
THE4RINGZ's avatar

THE4RINGZ

R.I.P Thread Bomber

16,816 posts
Jan 21, 2011 8:45 AM
Uhmmm hello this isn't a math problem because there are letters in it, not numbers.

I can't believe I am the only one smart enough to figure that out.
Jan 21, 2011 8:45am
Belly35's avatar

Belly35

Elderly Intellectual

9,716 posts
Jan 21, 2011 8:52 AM
Does not require the Talyor expanion
Jan 21, 2011 8:52am
J

jmog

Senior Member

6,567 posts
Jan 21, 2011 8:57 AM
Yes, that makes perfect sense.

I'm not sure what your supposed to do with the problem because you already have the answer...

Basically as x gets closer to zero (or the limit x->0), the -1/x^2 gets bigger and bigger and goes to negative infinity.

Well, when "e" (or any real number for that matter) is raised to a negative "big" number, its REALLY REALLY small. As the power goes to negative infinity the whole function goes to zero.

Now, if you are required to prove mathematically why that, I'd suggest L'Hopital's rule, if this is a calculus class and they already know derivatives.
Jan 21, 2011 8:57am
ZWICK 4 PREZ's avatar

ZWICK 4 PREZ

Senior Member

7,733 posts
Jan 21, 2011 9:14 AM
What exactly are you asked to do with this, b/c as jmog stated it's more of a statement than a problem.. unless you're asked to evaluate the limits.
Jan 21, 2011 9:14am
G

gut

Senior Member

15,058 posts
Jan 21, 2011 9:24 AM
Yeah, I think you probably just need to show the work. Been a long long time since I've done proofs, but you need to show the limit converges from the left and right of 0. Maybe let g(x) = (-1/x^2) and show that converges to -oo. Then f(x) = e^g(x) => 1/e^oo=>0
Jan 21, 2011 9:24am
justincredible's avatar

justincredible

Nick Mangold

32,056 posts
Jan 21, 2011 10:22 AM
gut;646562 wrote:Yeah, I think you probably just need to show the work. Been a long long time since I've done proofs, but you need to show the limit converges from the left and right of 0. Maybe let g(x) = (-1/x^2) and show that converges to -oo. Then f(x) = e^g(x) => 1/e^oo=>0

Alt+5 = ∞

Not a big deal or anything, just letting you know.
Jan 21, 2011 10:22am
G

gut

Senior Member

15,058 posts
Jan 21, 2011 10:55 AM
justincredible;646616 wrote:Alt+5 = ∞

Not a big deal or anything, just letting you know.

Haha....I thought I was pretty craft using the oo....Thanks for the tip, but doesn't appear to work on my keyboard.
Jan 21, 2011 10:55am
DeyDurkie5's avatar

DeyDurkie5

Senior Member

11,324 posts
Jan 21, 2011 11:00 AM
ccrunner609;646627 wrote:So what you are saying is that 70's all the way around is a 4:40?


(running joke....Said is a big time track start)

gay
Jan 21, 2011 11:00am
j_crazy's avatar

j_crazy

7 gram rocks. how i roll.

8,372 posts
Jan 21, 2011 11:32 AM
Rusty as I am at this, I think:

f'(x) = 2xe^(1/2x+1/(x^2))

therefore:

f'(0) = 2 * 0 * e ^(1/0+1/0) = 0*e^(∞+∞) = 0*∞ = 0
Jan 21, 2011 11:32am
J

jmog

Senior Member

6,567 posts
Jan 21, 2011 11:42 AM
j_crazy;646700 wrote:Rusty as I am at this, I think:

f'(x) = 2xe^(1/2x+1/(x^2))

therefore:

f'(0) = 2 * 0 * e ^(1/0+1/0) = 0*e^(∞+∞) = 0*∞ = 0

0*infinity does not necessarily=0. It can equal 0, infinity, and any number inbetween. Hard concept to understand, but its true.

Easiest example is the limit as x->0 of x*(1/x). That ends up 0*infinity right? However, the limit is 1, not zero.
Jan 21, 2011 11:42am
BigAppleBuckeye's avatar

BigAppleBuckeye

Senior Member

2,935 posts
Jan 21, 2011 11:49 AM
Jan 21, 2011 11:49am
J

jmog

Senior Member

6,567 posts
Jan 21, 2011 1:01 PM
BigAppleBuckeye;646733 wrote:

Funniest answer to a test I've seen, I know that one is "old", but it still is funny.

Oh, and everyone knows that x=5 on that one.
Jan 21, 2011 1:01pm
O-Trap's avatar

O-Trap

Chief Shenanigans Officer

14,994 posts
Jan 21, 2011 1:17 PM
x=justincredible
Jan 21, 2011 1:17pm
BigAppleBuckeye's avatar

BigAppleBuckeye

Senior Member

2,935 posts
Jan 21, 2011 1:36 PM
jmog;646875 wrote:Funniest answer to a test I've seen, I know that one is "old", but it still is funny.

Oh, and everyone knows that x=5 on that one.

I always liked this one too:

Jan 21, 2011 1:36pm
Heretic's avatar

Heretic

Son of the Sun

18,820 posts
Jan 21, 2011 1:36 PM
said_aouita;646512 wrote:lim as x->0 of f'(x) where f(x) = e^(-1/x^2) = 0

FFFFFFFUUUUUUUUUUUU
Jan 21, 2011 1:36pm