the last step should actually be two steps. first you factor out an h on the top... h(2x + h) and cancel it out with the h on the bottom. then your left with 2x + h, in which you can now substitute zero for the h which gives you 2x. the reason you couldnt make the substitution when the h was on the bottom is because it would make the denominator zero, which is a no no (this coming from a physics major and an mra) But the way you talk about math shows real promise. keep it up barb
I'm taking Calculus next semester (being a former liberal arts major, I never thought I'd be saying this.) I just started studying limits now, and I cant wait! (something else I never thought I would say.) Math is the shit. I always let my arts major friends know, once they get past the initial difficulty, math is fun, and they should give it a chance. Just doing my part to make everyone a little more employable.
I believe that you are supposed to cancel out the h's in the numerator and denominator before you make the approximation that h~0, otherwise 2hx would go to zero.
remember that h is a value, that is very close to, but never actually zero, so that for the purposes of calculating the instantaneous rate of change we can say that
2(0.0000000000001)(x) ≈ 2(0)(x) so h is never actually zero and wouldn't cause 2hx to result in zero due to multiplying by zero
Not really. l'Hospital's rule is ONLY applicable in determining if a continuous function has a derivitive at an arbitrary point on it's domain. It doesn't really help you FIND the derivitive because you still have to apply standard rules of differentiation just to use it. Heck, it doesn't even help you find the domain of the derivitve. It's almost like a tool you use to make sure you don't waste your time with an insolluble problem.
@Mathman1ac l'Hospital's rule changes 2hx + h^2 / h into 2x + 2h which makes it obvious that it is 2x as the limit goes to zero. It's similar to how dividing both sides by h gives 2x + h. l'Hospital's rule helps you solve limits, MrFalcon was talking about limits.
Incorrect. The change you are talking about above is algebra. In other words, if you didn't perform a differentiation, you are not using l'Hospital's rule.
But let's do some thing a bit different, What is the Limit (t->future) of f(t) = The Results of the "Feminist" Domestic Violence Industry Evil Indoctrination that is now Indoctrinated into Politics, the Government, Courts, Police and General Public, Encouraging an Epidemic of False Accusations of DV and Rape, that:
- Women are Good, Men are Bad!
- ..
- Women need Help and Protection, Men must be Restrained, Prosecuted and Jailed!
yeah the x's cancel out on the denominator, but i didnt mention it, since these math videos im going to be posting are going to be assuming some knowledge of calculus. im using pencil with a tablet not paint
true but then youd still be left with h^2/h = h ... i wanted to emphasize that the interval of f(x+h)-f(x) is small enough so that it could be considered an instantaneous rate of change
the last step should actually be two steps. first you factor out an h on the top... h(2x + h) and cancel it out with the h on the bottom. then your left with 2x + h, in which you can now substitute zero for the h which gives you 2x. the reason you couldnt make the substitution when the h was on the bottom is because it would make the denominator zero, which is a no no (this coming from a physics major and an mra) But the way you talk about math shows real promise. keep it up barb
tomtomvader 1 month ago
You need to consider teaching!
fomiz 2 months ago
I'm taking Calculus next semester (being a former liberal arts major, I never thought I'd be saying this.) I just started studying limits now, and I cant wait! (something else I never thought I would say.) Math is the shit. I always let my arts major friends know, once they get past the initial difficulty, math is fun, and they should give it a chance. Just doing my part to make everyone a little more employable.
sillygoose544 2 months ago
I believe that you are supposed to cancel out the h's in the numerator and denominator before you make the approximation that h~0, otherwise 2hx would go to zero.
MrFalcon675 2 months ago
@MrFalcon675
remember that h is a value, that is very close to, but never actually zero, so that for the purposes of calculating the instantaneous rate of change we can say that
2(0.0000000000001)(x) ≈ 2(0)(x) so h is never actually zero and wouldn't cause 2hx to result in zero due to multiplying by zero
barbarossaaaa 2 months ago
@barbarossaaaa i think he meant that you can simplify it a bit further to say:
(2hx + h^2)/h => h(2x + h)/h => 2x + h =>2x as h->0
thinfoxgmail 2 months ago
@MrFalcon675 He also could have used l'Hospital's rule as well because 0/0 is an indeterminate form. He skipped a step which was pretty self evident.
didles123 2 months ago
@didles123
Not really. l'Hospital's rule is ONLY applicable in determining if a continuous function has a derivitive at an arbitrary point on it's domain. It doesn't really help you FIND the derivitive because you still have to apply standard rules of differentiation just to use it. Heck, it doesn't even help you find the domain of the derivitve. It's almost like a tool you use to make sure you don't waste your time with an insolluble problem.
Mathman1ac 2 months ago
@Mathman1ac l'Hospital's rule changes 2hx + h^2 / h into 2x + 2h which makes it obvious that it is 2x as the limit goes to zero. It's similar to how dividing both sides by h gives 2x + h. l'Hospital's rule helps you solve limits, MrFalcon was talking about limits.
didles123 2 months ago
@didles123
Incorrect. The change you are talking about above is algebra. In other words, if you didn't perform a differentiation, you are not using l'Hospital's rule.
Mathman1ac 2 months ago
@barbarossaaaa :
Great Video ! Thanks !
But let's do some thing a bit different, What is the Limit (t->future) of f(t) = The Results of the "Feminist" Domestic Violence Industry Evil Indoctrination that is now Indoctrinated into Politics, the Government, Courts, Police and General Public, Encouraging an Epidemic of False Accusations of DV and Rape, that:
- Women are Good, Men are Bad!
- ..
- Women need Help and Protection, Men must be Restrained, Prosecuted and Jailed!
MarthaLauraGranados6 2 months ago in playlist More videos from barbarossaaaa
Been a while since I was shown the method for differentiating from first principles like this. Kinda forgot all about it.
j1mmyZeta 2 months ago
Comment removed
Washingstone 2 months ago
@Washingstone
yeah the x's cancel out on the denominator, but i didnt mention it, since these math videos im going to be posting are going to be assuming some knowledge of calculus. im using pencil with a tablet not paint
barbarossaaaa 2 months ago
This reminds me of PatrickJMT.
theignoredgender 2 months ago
We need more very smart and logical men in the world like you Barb!!
k5lta 2 months ago
This channel just got from best to priceless.
Thank You!
Static172 2 months ago
Comment removed
Static172 2 months ago
Um.. Dude the h's are supposed to cancel eachother out. If you just said they were equal to zero it would be 0/0
mikemustmurder 2 months ago
@mikemustmurder
true but then youd still be left with h^2/h = h ... i wanted to emphasize that the interval of f(x+h)-f(x) is small enough so that it could be considered an instantaneous rate of change
barbarossaaaa 2 months ago
@mikemustmurder
You're taking the limit as h approaches 0. So h is never actually 0, it's just getting closer and closer to it. 0/0 is undefined.
theignoredgender 2 months ago
Barbarosa, what are you going to school for to use this math?
ApollosInsight 2 months ago
@ApollosInsight
chemical engineering, but the practical applications of this process are boundless.
barbarossaaaa 2 months ago
@barbarossaaaa Just curious, here. In your chemical engineering classes, do you use any textbooks by JD Seader? He's a friend of my family.
Ersa1a 2 months ago