9 ай бұрын
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2 жыл бұрын
2 жыл бұрын
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2 жыл бұрын
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@user-ez2zy1ky4p 7 күн бұрын
The cross-section of a drain is to be an isosceles trapezium, with three sides of length 2 metres, as shown. Find the angle θ that maximises the cross-sectional area, and find this maximum area.
@noone7692 15 күн бұрын
Hello, I have a simple and dumb question to ask. Why are we changing the integral f(x)dx from limit [a,x] to a dummy variable f(t)dt. To put it clear why are we using the dummy variable t u or v specifically ?. What will the consequences if we still integrste without changing it to the dummy variable?
@slcmathpc 14 күн бұрын
It is to avoid what is commonly known as a "clash of variables". The actual variable in this instance is the upper bound of integration, which we chose to label as "x". The variable, say "v", in the integrand "f(v)dv" is what is known as a "dummy variable", since it is not a consequential variable and is completely independent of the upper bound of integration "x". Writing the integrand "f(v)dv" as "f(x)dx" seems to suggest that the "x" in "f(x)dx" has something to do with the upper bound of integration "x", which is simply not the case. Writing the integrand as "f(x)dx" and using "x" as the upper bound of integration causes a "clash" between the two expressions, which again, have nothing to do with one another. Hope this clears things up!
@noone7692 14 күн бұрын
@@slcmathpc thank you
@stevenkaban 15 күн бұрын
thank you very much for proving a lot of infinite series' tests to the world
@FaizMuhammadsahto 18 күн бұрын
Excellent sir ❤
@user-ey3oy4rw8o 18 күн бұрын
Neat and dainty hand writing. 👍It would be great if you can explain it.
@yuutek4165 23 күн бұрын
How did you get that with any x, f(x)=(x-a)q(x)+f(a) if f(a)=C only when x=a?
@slcmathpc 18 күн бұрын
Since C is a constant, then it must be the same for any value of x chosen.
@Historyvlogsbyfaiz123 24 күн бұрын
Thanks ❤
@mvas1l Ай бұрын
45:27 shouldnt the last element of v3 be 1 since you didnt scale it?
@shekharjoshi7292 Ай бұрын
Such a clear derivation. Realy amazing.
@RanBlakePiano Ай бұрын
I can t hear you
@salmonroe5608 Ай бұрын
thank you dear sir for this demonstration. It helped me review my studies. Have a great day.
@Victual88 Ай бұрын
Thanks Man for the great proof! minor correction at 1:20 (you wrote + said (AB) is a P x M matrix. I think you meant (AB)^T is a P x M matrix. (It's still definitely clear what you mean btw)
@LorettaAhenkan-bi9hb Ай бұрын
you said cube root of negative is negative so why did you write x not -x
@slcmathpc Ай бұрын
Because x is negative. ;-)
@AlfredKatema-fg1qe Ай бұрын
Where did you get those figures 7,10,15 and 22 because when I square matrix a Am getting those figures
@ObiajuluEmma-Ebere 2 ай бұрын
Excellent!! From Nigeria, thank you.
@Vedant-xf9qn 2 ай бұрын
bro does not get enough credit
@Johnsonmoses-hp1kz 2 ай бұрын
Me the question is not stated befor sloving how i meant going to understand
@Sarah._.s889 2 ай бұрын
Very clear and well explained Thank you very much🙏
@chrisprice8547 2 ай бұрын
Amazing. Helped me with my Uni assignment. Much love.
@DeepanM-xm6fn 2 ай бұрын
Well explanation
@ronimandiviiia2514 2 ай бұрын
Ya bro, it was really nice to understand this basic problem. Thank you so much to describe this in easy and brief manner. Just keep it up.😊
@tarekbouchlaghem7277 2 ай бұрын
Thanks for the simplification
@eiconmatheus6812 2 ай бұрын
I am starting to hate school especially when math is included
@teslayt940 2 ай бұрын
Explained a 3hr lecture in less than 1hr
@sumsumiho 2 ай бұрын
Thank you so much for such a detailed and easy-to-follow explanation!
@Emma-ki3fv 3 ай бұрын
This is the first time I understood this thank you, it’s been 2 months since my professor taught it.
@HannahDavies-dp6qn 3 ай бұрын
in final step, is the tangent line slope calculation mean to say f(x)dx /g(x) dx evaluated at c (not the derivatives) thank you
@slcmathpc 3 ай бұрын
It is indeed f'(x)dx/g'(x)dx evaluated at x=c.
@kungfooman 3 ай бұрын
What if you have x and x squared in the equations? If you define x squared to be... lets say... "a", then the non-squared x turns into a square root and it's still non-linear?
@slcmathpc 3 ай бұрын
Not every non-linear system can be effectively turned into a linear one; it only works for "slightly non-linear" systems. Of course, in your example, you could let a=x and b=x^2, and if the system can then become linear, you can solve it, but at the end, you would have to check that the values of a and b obtained are consistent with the fact that b=a^2.
@kungfooman 3 ай бұрын
@@slcmathpc Thank you for the feedback, my example system is: (1) x²+y²=125 and (2) x+y=15... we can already see that it's {x=10,y=5} and vice versa. But I fail to find a nice way to turn it into a linear system, even tho the answer already seems so obvious/simple. My best hope was: let a=a+y, b=xy and take the binomial form of (1) which is (3) (x+y)²-2xy. Then we will have as a result: a²-2b=125 and a=15 and if you solve that you get {a=15, b=50} which is correct since a=x+y=10+5=15 and b=x*y=10*5=50. Still not linearly solvable... maybe it's an example of a non-slightly non-linear system? Lol
@Festus2022 3 ай бұрын
Great explanation. Thanks
@user-wp3fu7eu1d 3 ай бұрын
Real Goat
@YonatanHaile-rf2jm 3 ай бұрын
this video was gonna make me question the things i know about this topic, I don't recommend this video
@JnSubli 3 ай бұрын
Hi, My understanding for series to diverge is when "nth divergence test" must also meet this criteria lim n→∞ aₙ = lim n→∞+1 aₙ ......= lim n→∞+∞ aₙ ≠ 0 else they would either Diverge (don't summed up to a real number) or Undefined (if all summed up to zero and infinitely repeating). Example for aₙ terms that are lim n→∞ (-1)^n or lim n→∞ sin(n) is Undefined. And for your case above lim n→∞ |aₙ| = ∞ ⇒ lim n→∞ aₙ ≠ 0 it may not meet lim n→∞ aₙ = lim n→∞+1 aₙ because lim n→∞ aₙ and n→∞+1 aₙ could also be +- aside from ++ or -- according to the ratio test |aₙ₊₁/aₙ| > 1. It Diverge only because the terms didn't summed up to zero. What do you think sir?
@fidget5437 3 ай бұрын
Ten/ten video, helps out a ton! Props for putting in the work to make this video's explanation perfectly comprehensible.
@user-mn2mc3pd4d 3 ай бұрын
thanks
@hulusiserdaryldrm8854 3 ай бұрын
i was like WTF ?!? when i saw she is a male then i realized that he said we should correct it with "person" lol
@hulusiserdaryldrm8854 3 ай бұрын
but after a 10 years , thanks a lot ! you made me understand this topic which other 5 videos failed to do :D
@Tukskun 3 ай бұрын
thank you boss
@ahmadfakhir7410 3 ай бұрын
Thanks very good example👍💖💚
@IlayShriki 3 ай бұрын
A great video!
@Someone_Named_GlowingSubspace 3 ай бұрын
Did somebody call my name?
@jamesboumalhab7337 3 ай бұрын
Appreciate you g
@user-sm7ru4vu2b 4 ай бұрын
Great vid
@helbertrodriguez6449 4 ай бұрын
absolute legend
@lunaticnomad0 4 ай бұрын
Nice content, was a great refresher for me!
@MOHINIVERMA-cp5ey 4 ай бұрын
best vedio on this topic
@jenm1 4 ай бұрын
flawless vid
@abhinaba9190 4 ай бұрын
I found your derivation to be very helpful.....but I have just one question..... The graph a displacemnt-time graph right?
@slcmathpc 4 ай бұрын
Yes, you should think of f(t) as the position of an object moving in a linear fashion as a function of time. :-)
@abhinaba9190 4 ай бұрын
So that means the position of the object is in a continuous function of time.....like for example for a free falling body changing its postion or accelerating uniformly in the influence of gravity.....with change in time.....
@slcmathpc 4 ай бұрын
Yep, those are valid examples!
@abhinaba9190 4 ай бұрын
Thank u:-)
@user-kp2uk3cg4g 4 ай бұрын
Thank you prof for the wonderful explanation. I study in Stanford; according to people our faculties are world class. However, I could not understand 1/10th of what I understood here.
@surendrakverma555 4 ай бұрын
Very good. Thanks
@errorhostnotfound1165 4 ай бұрын
I know that he said that finding the generic formula for i^k is supposed to be an exercise, but I have gotten stuck at (n+1)sum((2i-1)^(k/2)) - sum(i(2i-1)^(k/2)), so what is it? I haven't been able to find anything online so far
@slcmathpc 4 ай бұрын
The idea that I have presented in these videos only allows one to find the summation formula for i^k recursively, so you can find that of i^3, then i^4, then i^5, and so on, but you cannot jump to say i^20, without first finding the formula for all of the powers lower than 20. Hope this clarifies things. :-)
@lesserafimseason 4 ай бұрын
God I swear this helped me understand the concept better thanks so much.