Thank you so so much for these videos! I've done my A levels maths several years ago and have forgotten most of the stuff (but really didn't forget much, because I haven't really learnt much in the first place, it was all procedural learning at that time). Now I am relearning (well actually learning it "properly") to enable me to learn statistics, specifically, I am learning the proofs of propositions in the theory of Maximum Likelihood Estimation.Your videos make me understand so much better and made me like maths like never before.
Thanks so much for making this video! I use your videos for a great little summary of what I did in my lesson and I can tel they'll be great revision later on.
do you have any techniques on conceptualising maths. I definitely want to know all this, however almost everything just goes over my head. I believe its because I have no context to references/concepts. sorry if this is a daft question, any help would on this would be MASSIVELY appreciated!
Hey jack, so in college we learnt a way of finding areas under a curve or line using the ‘trapizium rule’ and this had a particular equation in which we need to know... I was wondering if you have any videos of this at all? Thanks
Hi thanks for the video, I'm struggling to understand why f(x)=(A(x+h)-A(x))/h as if h tends to 0 this then surely it should disappear just like the extra part?
Good afternoon, sorry to bother you but I would really appreciate it if you could help me with this question: f '(x)=(1-2x^1/3)^3 Given that f(8)=24, find f(1) Thanks
I don’t really understand what f(x) actually is I thought it was just function/equation for a curve or line also could you elaborate 10:13 to 13:07 I don’t really understand how the 1st principles f’(x) equates to all of that
f'(x) is the first derivative of the f(x) which could any function. Its difficult because most times f(x) is used but as far as i am concerned it is just a function Hope this helps
What you've got to clock onto is that we don't know the area of that little extra bit of the curve, but it is definitely smaller than the rectangle. If we can show that the rectangle tends to zero as h tends to zero, then anything smaller than it (inside) must do the same.
Yes, the part of the spec is here: sites.google.com/site/tlmaths314/home/a-level-maths-2017/full-a-level/h-integration/01-fundamental-theorem-of-calculus "Know and use the Fundamental Theorem of Calculus". Essentially, what that means is that you need to know that evaluating an integral between two limits is the area under the graph - you won't be asked to replicate the theorem.
TLMaths because we defined A(x) as the area from x = 0 to x, to find the until x=a in my scenario would surely be A(a) ? (Sorry about all the questions)
By definition of A(x) being the area from x=0 to x, the consequence of this is that A(0) = 0. But in general when integrating from x=a to x=b, the area would be A(b) - A(a)
![A-Level Maths: H2-01 [Integration: Integrating ax^n]](http://i.ytimg.com/vi/ZFz5ybkKVIY/mqdefault.jpg)
![A-Level Maths: H2-01 [Integration: Integrating ax^n]](/img/tr.png)
Thank you so so much for these videos! I've done my A levels maths several years ago and have forgotten most of the stuff (but really didn't forget much, because I haven't really learnt much in the first place, it was all procedural learning at that time). Now I am relearning (well actually learning it "properly") to enable me to learn statistics, specifically, I am learning the proofs of propositions in the theory of Maximum Likelihood Estimation.Your videos make me understand so much better and made me like maths like never before.
When are you expecting to have all videos in this playlist completed for?
You've done well to get so many out so quickly.
Thanks - I have no idea when it'll all be done, but I'm pretty sure I'm past half way.
Great explanation sir, your teachings are very helpful, many thanks.
Glad I can help! Thanks for watching!
Thanks so much for making this video! I use your videos for a great little summary of what I did in my lesson and I can tel they'll be great revision later on.
do you have any techniques on conceptualising maths. I definitely want to know all this, however almost everything just goes over my head. I believe its because I have no context to references/concepts.
sorry if this is a daft question, any help would on this would be MASSIVELY appreciated!
Drawing diagrams - I find that very important in understanding what's going on
@@TLMaths thank you very much!
and great work with the videos btw!
Hey jack, so in college we learnt a way of finding areas under a curve or line using the ‘trapizium rule’ and this had a particular equation in which we need to know... I was wondering if you have any videos of this at all? Thanks
The Trapezium Rule videos are here: sites.google.com/site/tlmaths314/home/a-level-maths-2017/full-a-level/i-numerical-methods/03-numerical-integration
Hi thanks for the video, I'm struggling to understand why f(x)=(A(x+h)-A(x))/h as if h tends to 0 this then surely it should disappear just like the extra part?
oh i just got it XD
"might not be gasping of air" made be crackle
Absolutely bloody brilliant!
This is why ur a legend
lovely vid and great explanation
Why does deltax become dx in the last part?
Good afternoon, sorry to bother you but I would really appreciate it if you could help me with this question:
f '(x)=(1-2x^1/3)^3 Given that f(8)=24, find f(1)
Thanks
Expand brackets:
f'(x) = (1-2x^(1/3))^3 = 1 - 6x^(1/3) + 12x^(2/3) - 8x
Integrate:
f(x) = x - (9/2)*x^(4/3) + (36/5)*x^(5/3) - 4x^2 + c
sub in condition:
24 = 8 - (9/2)*8^(4/3) + (36/5)*8^(5/3) - 4*8^2 + c
so:
c = 568/5
Then
f(x) = x - (9/2)*x^(4/3) + (36/5)*x^(5/3) - 4x^2 + 568/5
Finally:
f(1) = 1133/10
I don’t really understand what f(x) actually is I thought it was just function/equation for a curve or line also could you elaborate 10:13 to 13:07 I don’t really understand how the 1st principles f’(x) equates to all of that
f'(x) is the first derivative of the f(x) which could any function. Its difficult because most times f(x) is used but as far as i am concerned it is just a function
Hope this helps
I'm not quite sure I understand why we divide the area of the rectangle by h?
I rearrange to get f(x)= at 6:11, which in turn divides the extra bit by h.
i don't get it...why we need to divide the area of rectangle by h?
I rearrange to get f(x)= at 6:11, which in turn divides the extra bit by h.
(f(x+h)-f(x))h is the extra bit. So do the same to it as in the f(x) equation
Is the extra part the little rectangle or just the shaded part in it?
What you've got to clock onto is that we don't know the area of that little extra bit of the curve, but it is definitely smaller than the rectangle. If we can show that the rectangle tends to zero as h tends to zero, then anything smaller than it (inside) must do the same.
TLMaths thanks 👍
im doing my first year and i have an exam next week on the 18/12/2020 will I need to know this for that.....
I don’t know what’s on your test?
Does this still count for the new syllabus?
Yes, the part of the spec is here: sites.google.com/site/tlmaths314/home/a-level-maths-2017/full-a-level/h-integration/01-fundamental-theorem-of-calculus "Know and use the Fundamental Theorem of Calculus". Essentially, what that means is that you need to know that evaluating an integral between two limits is the area under the graph - you won't be asked to replicate the theorem.
yeah
Wouldn't H move closer and closer to the origin on the X axis when you take away X?
h is the gap between x and x+h - it is the gap that is getting smaller. We're not moving everything to the origin.
@@TLMaths Ah, thanks for the help and the quick reply
If f(x) = A’(x) does that mean integral of f(x) = A(x) ?
There's a constant of integration in there, but essentially yes
TLMaths since A(x) = integral of f(x) + c, if we subbed x = a into this it would find the area under the curve f(x) between x = a and x = 0 ?
So the area would A(a) - A(0)
TLMaths because we defined A(x) as the area from x = 0 to x, to find the until x=a in my scenario would surely be A(a) ? (Sorry about all the questions)
By definition of A(x) being the area from x=0 to x, the consequence of this is that A(0) = 0. But in general when integrating from x=a to x=b, the area would be A(b) - A(a)
Hi, do we need to know this for AS ?
Yes you should be aware of this
Is this studied in UK after 10th ?
The 10th what?
@@TLMaths 10th grade
It's material you would meet after GCSE Maths, which is studied up to age 16, in A-Level Maths, if that helps?
i dont get it lol
What can I help with?
@@TLMaths i know now ty