said_aouita
Posts: 8,532
Jan 21, 2011 7:06am
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
Does this make sense to you?
lim as x->0 of f'(x) where f(x) = e^(-1/x^2) = 0
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september63
Posts: 5,789
Jan 21, 2011 8:40am
What you talkin bout, Willis?
THE4RINGZ
Posts: 16,816
Jan 21, 2011 8:45am
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.
I can't believe I am the only one smart enough to figure that out.
Belly35
Posts: 9,716
Jan 21, 2011 8:52am
Does not require the Talyor expanion
J
jmog
Posts: 6,567
Jan 21, 2011 8:57am
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.
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.
ZWICK 4 PREZ
Posts: 7,733
Jan 21, 2011 9:14am
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.
G
gut
Posts: 15,058
Jan 21, 2011 9:24am
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
justincredible
Posts: 32,056
Jan 21, 2011 10:22am
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.
G
gut
Posts: 15,058
Jan 21, 2011 10:55am
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.
DeyDurkie5
Posts: 11,324
Jan 21, 2011 11:00am
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
j_crazy
Posts: 8,372
Jan 21, 2011 11:32am
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
f'(x) = 2xe^(1/2x+1/(x^2))
therefore:
f'(0) = 2 * 0 * e ^(1/0+1/0) = 0*e^(∞+∞
= 0*∞ = 0
J
jmog
Posts: 6,567
Jan 21, 2011 11:42am
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*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.
BigAppleBuckeye
Posts: 2,935
Jan 21, 2011 11:49am
J
jmog
Posts: 6,567
Jan 21, 2011 1:01pm
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.
O-Trap
Posts: 14,994
Jan 21, 2011 1:17pm
x=justincredible
BigAppleBuckeye
Posts: 2,935
Jan 21, 2011 1:36pm
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:
Heretic
Posts: 18,820
Jan 21, 2011 1:36pm
said_aouita;646512 wrote:lim as x->0 of f'(x) where f(x) = e^(-1/x^2) = 0
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