Відео

I don't even know why I'm watching this.

Tried solving using desmos. Plotted x+y=8 first. Then plotted x^y = some constant b. The value of b where the two graphs only have one point of intersection is the maximum value of the function, and that came out to be approximately 280.902799

Isnt last one sin(π/2+2πk) which always will give one and sin(-3π/2+2πk) which will also end on the positive side of the circumference as its going to the negatives and then the postives? Reasoning like that it would be 1+1 =2

guys jokes aside but how do you know that the limit of a continuous function is a function of the limit of the thing inside it? Is it calc 1 or 2 or 3? I dont remember getting this property when learning limits. Tanks

log base 1 does not exist...

Sir videos help me a lot to make my concept very strong in mathematics love from India❤❤❤❤

The easiest way to calculate sin 15 is sin (45-30) = sin 45cos 30 - cos 45sin 30. 45 and 30 are special angles.

If in doubt iterate! Here are 2 iteration equations for 2 real roots anyway. Use x = 1 to start things off x^5 - 5x + 3 = 0 x^5 = 5x - 3 x = (5x - 3)^(1/5) 1.275 682 204 x^5 - 5x + 3 = 0 x^5 - 5x = -3 x(x^4 - 5) = -3 x = -3/(x^4 - 5) 0.618 033 988 8 (Golden Mean)

I have a question, arctan (♾️) is not only equal to π/2, it also can be 5π/2, how do you prove that π/2 is the unique answer? Thanks

I’m too late for this but ever considered adding sinh(x) cosh(x) tanh(x) coth(x) etc, to the integral?

I like how my professors doesn't taught me this 🙃 Thank you professor, you are very useful

11:41

For each of them you could just multiply both sides by (x-1) for instance: (x-1)(x³+x²+x+1) = (0)(x-1) x⁴-1 = 0 x⁴ = 1 and therefore x = 1 ∠ θ Where θ = 0°,90°,180°,270° Except when θ = 0 we would have x = 1 which is an artifact created when multiplying by x - 1 and not a genuine solution

hey man how did you derive the 2 equation i am having a lot of trouble understanding that . how did you remove mod from the equvalence and all that

√i = √me if you square bothe sides i = me. Therefore i am me.

we can solve by adding the equations xy+z=40 eq1 xz+y=51 eq2 x+y+z=19 eq3 on adding eq. 1,2,3 x+xy+xz+2y+2z=110 adding 2 on both the sides x(y+z+1) 2(y+z+1)=112 (x+2) (y+z+1)=112 -------equation 4 from equation 3 y+z=19-x substituting y+z=19-x in eq. 4. (x+2) (-x+20)=112 -x^2+18x-72=0 (x-6)(-x+12)=0--------equation 5 from equation 5 x=6, x=12 substituting x=6 in equations 1,2,3 we get 6y+z=40--eq6 6z+y=51---eq7 6+y+z=19 --eq8 from equation 8 y+z=13 from equation 6 z=40-6y substituting z=40-6y in eq. 8 -5y=-27 y=5.4 substituting y=5.4 in equation 8 z=7.6

I found this formula through recursion once, and also number of squares

you didn't miss a single step, it got way easier to understand

I saw the blue pen 😂

Wow, I'm really glad I watched that video on Euler's equation, otherwise this video would be gibberish.

Welcome

Pls make the proof for sqrt of a+sqrt of a - sqrt of a so on

When you really really love this question

You should try the 2011 IMO question number 2 it is very fun

Somewhere around 24/25

All 5 solutions of the original equation (0, two positive and two negative) are valid. For angles: { 0, 36, 72, 108, 144 } + k * 180 for integer k including zero. For an even k they are 0 or positive and for an odd k they are 0 or negative.

why cant you just write the sin(x) as cos(x-pi/2)

within like 5 seconds of me thinking about it, I was like "y=1" but was also like "that is definitely correct, but way too simple for this to be the answer he gives" lol

Feynman's Trick or Leibniz Rule ?

This is very brilliant

It's not that hard, it's just a sector of a circle = (1/3)pi×4^2 MINUS Area of triangle= (1/2)absinC = (1/2)×4^2×sin120 = 8×sqrt(3)/2 = 4sqrt(3) Then just a full circle minus 4 of those D shapes, easy.

I think the first step is the reason why this equation truly does not have a solution as a logarithm to the base 1 is not defined (not even in the complex world)

I was part of the year this question was on 😭

i = EXP(i*Pi/2) or i = EXP(i*(Pi/2+2*Pi)) --> SQRT(i) = EXP(i*Pi/4) or EXP(i*5*Pi/4) --> SQRTi) = Cos(Pi/4) + i Sin(Pi/4) or Cos(5*Pi/4) + i Sin(5*Pi/4) --> SQRT(i) = SQRT(2)/2 + i * SQRT(2)/2 or SQRT(i) = -SQRT(2)/2 - i * SQRT(2)/2

3:32:45 tan θ is wrong, you forgot thats 4x not 4

U r so smart Thank you 💗

11:55 that transition

george washington

I need this calculateor please🙏

OMG, seeing these questions bring me back memories of me sitting in front of the desk in my room, doing past papers after past papers. Just missed mine by 6 years (Jun 2016)

I know I am 5 years late for the party, but shouldn't integral number 31. equal to: -4*sqrt(1-sqrt(x)) + C?

This video deserves the word "ultimate"

i was having a hard time reviewing my instructor's pdf, thank you for this!~

∆ABC, AB=AC=1 and ∠A=36° Let D is on AC such that AD=BD then ∠BDC=∠C=72° and ∆ABC~∆BCD (AA) Let AD=BC=a ( cos72°=√[1-(a/2)²] ) then 1:a=a:(1-a) => a²=1-a => a=(-1+√5)/2 Thus cos72°=√(a+3)/2 =√[2(5+√5)]/4

Thank u sir

The no.1 confused me b/c I interpreted log as base 10. Also why do they make ln notation if people still use log for ln anyway?

This video 'I hate internet math' by doorwaydude is what I consider to be a 'sequel' to this vid. It attempts to explain why these debates exist in the first place (and why some of them are pointless). I really think people in this comment section should have a look if they are still unsure about things like 0.999...=1

So it doesn't change the fact that I don't like minus and I remove it, and I am still correct

But wait what about limits like lim(1/x) as x->0? From one side it approaches +inf and from another -inf. L'Hopital would say it's equal to 0 but I think most people would still say it's undefined/indeterminate?

Find Sin(1), multiply by 72 and you're set! /s