Prime Newtons
Prime Newtons
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Regional Math Olympiad Problem
This is from the Regional Math Olympiad. The trick here is that not all polynomials are solved in terms of x. Sometimes the other unknown variable becomes the key.
zhlédnutí: 4 062

Video

Invoking the Gamma Function
zhlédnutí 4,4KPřed 4 hodinami
This definite integral could not be evaluated using the integration techniques learned in calculus2. I showed that the problem could be modified by appropriate substitution to facilitate the use of the gamma function for its evaluation.
An exponential trig equation
zhlédnutí 2,6KPřed 7 hodinami
This was a problem from the Canadian Euclid Math Contest from 2024 . A 12 grader is expected to easily answer this question without requiring any special knowledge or reasoning.
x - 1/x² = (rad2)i , Find x^2187 - 1/x^2187.
zhlédnutí 3,1KPřed 7 hodinami
This was a multiple choice problem from Jee Admanced sent in by a subscriber. The required skills were basic algebra and a drop of keen observation.
2024 Canada Euclid Math Contest
zhlédnutí 5KPřed 9 hodinami
The main idea was to use the laws of logarithms and then some multiplication and division. It was a good problem to wreslte with for any 12th-grade student.
The Last 3 digits of sqrt( 1^3 + 2^3 + ...+ 2024^3)
zhlédnutí 4,4KPřed 12 hodinami
The main idea was to use the fact that the sum of n natural cubes is the square of the sum of n natural numbers. This is the video on the proof referred to in the video czcams.com/video/VgwLVxLoLz0/video.htmlsi=DLy8qqhh0NMOJDvE
Team Selection Test (Ecuador 2008)
zhlédnutí 5KPřed 14 hodinami
This system of equations could be easily solved by inspection or algebraic substitution. It is only necessary to find all solutions.
A problem from Denmark 2006 (Georg Mohr)
zhlédnutí 4,9KPřed 14 hodinami
This problem is quite easy considering the algebra and level of reasoning involved in the solution I gave. After finding one set of solution, It was required to show that there were no other solutions.
Position, Jerk, Pop and Other Derivatives of The Position Function
zhlédnutí 3,4KPřed 19 hodinami
Whenever we discuss motion, we often talk about position, velocity and acceleration. in this video, i introduced the audience to higher derivatives of the position function such as the jerk, which is the change in acceleration with time. Other derivatives were the snap/jounce, crackle and the pop.
Lim (1+x^9)/(1÷x^13) as x app -1
zhlédnutí 8KPřed 21 hodinou
Lim (1 x^9)/(1÷x^13) as x app -1
How to depress a cubic
zhlédnutí 7KPřed dnem
The cubic formula is rarely used and rarely talked about. This video explains how to depress a cubic polynomial into a form that works with the cubic formula. Watch Cube-root of Unity here: czcams.com/video/lHe6iieqzBw/video.htmlsi=n7MZFf6ALc4giVnU
Cubic Formula for Depressed Cubic
zhlédnutí 7KPřed dnem
The cubic formula is rarely used and rarely talked about. This is a very effective formula fpr computing the roots of a depressed cubic equation - A cubic missing the quadratic term. In this, video I showed a simple derivation of the formula by reverse engineering.
JEE Advanced 2022 #2
zhlédnutí 6KPřed dnem
This this limit problem is the limit of a composition of trig and logarithmic function. The main idea is to know how to compose the functions and take the limit of the composed function as the function of the limit.
1961 IMO #1
zhlédnutí 4,5KPřed 14 dny
This was question 1 in the 1961 IMO in Hungary. I have made an attempt at solving this algebra problem using basic high school reasoning. Hope it makes sense.
Belphegor's Prime
zhlédnutí 5KPřed 14 dny
This is a palindrome beastly prime number. it contains the number 666 and strange forms of the number 13. It was discovered by Harvey Dubner and named by Clifford Pickover after one of the Seven Princes of Hell in his book.
Tens digit of 3^2024
zhlédnutí 4,4KPřed 14 dny
Tens digit of 3^2024
A set Theory problem from JEE Advanced 2022
zhlédnutí 3,1KPřed 14 dny
A set Theory problem from JEE Advanced 2022
Third International Mathematics Olympiad #2
zhlédnutí 8KPřed 14 dny
Third International Mathematics Olympiad #2
Find the last digit of (1! + 2! +...+ 1982!)^1982
zhlédnutí 10KPřed 14 dny
Find the last digit of (1! 2! ... 1982!)^1982
Prove that abcd = 2004
zhlédnutí 9KPřed 14 dny
Prove that abcd = 2004
A nice Completing the squares problem
zhlédnutí 4,5KPřed 14 dny
A nice Completing the squares problem
Evaluate z^2024 + 1/z^2024 Given that z+1/z=1
zhlédnutí 33KPřed 21 dnem
Evaluate z^2024 1/z^2024 Given that z 1/z=1
Identifying the graphs of a function and its derivatives
zhlédnutí 3,1KPřed 21 dnem
Identifying the graphs of a function and its derivatives
Evaluating a series of factorials
zhlédnutí 7KPřed 21 dnem
Evaluating a series of factorials
A Non-palindromic Quartic Equation
zhlédnutí 7KPřed 21 dnem
A Non-palindromic Quartic Equation
Solving a radical polynomial with trig substitution
zhlédnutí 9KPřed 21 dnem
Solving a radical polynomial with trig substitution
2015 Harvard-MIT Math Tournament #25
zhlédnutí 15KPřed 21 dnem
2015 Harvard-MIT Math Tournament #25
Maclaurin Series for 2^x
zhlédnutí 7KPřed 28 dny
Maclaurin Series for 2^x
Sum of the roots of a 2001st power polynomial
zhlédnutí 10KPřed měsícem
Sum of the roots of a 2001st power polynomial
Vieta's Formula
zhlédnutí 11KPřed měsícem
Vieta's Formula

Komentáře

  • @williampeters71
    @williampeters71 Před 13 minutami

    listened again getting clearer we assume a delta less than 1 what if the limit of the function dne then this would be false

  • @attackhelicopteriscool

    watching this video makes me feel smart in mathematic but when i tried to solve an easy looking algebra, i don't even know what to do first 😂😂

  • @physicsclasswithputisir5594

    Excellent

  • @VictorJunyiWang
    @VictorJunyiWang Před hodinou

    Use sec(x) squared = 1 + tan(x) squared to get sec(x) squared is always greater than 1

  • @physicsclasswithputisir5594

    Great❤

  • @Mr.FelixBlazTube
    @Mr.FelixBlazTube Před hodinou

    Sir can you find all real and complex solutions for this polynomial equation which has fractional powers that is X^{4/3} - 4X^{2} + 4 = 0

  • @yajatyadav8029
    @yajatyadav8029 Před 2 hodinami

    2^2^2=16 lmao I'm now mathematician😅😅

  • @souverain1er
    @souverain1er Před 2 hodinami

    It is easier to optimize the square of the area

  • @ayushrudra8600
    @ayushrudra8600 Před 3 hodinami

    I think jp maths made a video on this recently...

  • @robertveith6383
    @robertveith6383 Před 3 hodinami

    The microphone was not good in this video. I noticed because my volume was turned up all the way.

  • @sunil.shegaonkar1
    @sunil.shegaonkar1 Před 3 hodinami

    I found the value of XY from equation 1 and then substitute it in equation 2, that gives equation similar to hyperboloid: x^2 + y^2 +2Z^2 = 6 - cut by a plane x+ y = 2. No Other point than (1 1 0).

  • @JamesJames-xp4xp
    @JamesJames-xp4xp Před 3 hodinami

    Like seriously thx vry much

  • @the_real_nayak
    @the_real_nayak Před 4 hodinami

    As an Indian, we do this in 11th STD

  • @dougaugustine4075
    @dougaugustine4075 Před 4 hodinami

    I found this right after watcching your second video from four years ago about finding the last digit (as opposed to multiple last digits as in this video). I learned two new concepts here that were not in the other video. Presentation was really polished too.

  • @dougaugustine4075
    @dougaugustine4075 Před 5 hodinami

    I was looking over your videos and saw this one. Your current presentations have really become polished in contrast.

  • @MichaelIfeco-tj1jc
    @MichaelIfeco-tj1jc Před 5 hodinami

    What if it's a cube root or even a fourth root

  • @haroldosantiago819
    @haroldosantiago819 Před 5 hodinami

    Thanks teacher... U relaly have a good heart

  • @Nobodyman181
    @Nobodyman181 Před 5 hodinami

    Prime Newtoon's owner, how to find d^i/dx^i, when i is imaginary number?

  • @Gold3nGallina
    @Gold3nGallina Před 6 hodinami

    16

  • @skwervin1
    @skwervin1 Před 6 hodinami

    2 to the power of 2 to the power of 2 2 to the power of 2 = 4 then 2 to the power of 4 = 2x2x2x2 = 16 ohhhh.... I like this sort of maths!

  • @user-zg8ny5tp4g
    @user-zg8ny5tp4g Před 6 hodinami

    Please, can you explain what exactly the Feynman technique, with simple exercise

  • @frankvanhertrooij5581
    @frankvanhertrooij5581 Před 6 hodinami

    I solved this problem using derivation. We know that the graph of f(x) needs to intersect the x-axis at 4 points for there to be 4 real solutions. Between each of these points, there is a local minimum or maximum, which means that the derivative of the function has to intersect the x-axis at at least 2 points. To find out under which conditions this is true, we find an expression for the x-value of the local minimum of f'(x) by setting the second derivative to 0: f''(x)=0. This yields an x-value of sqrt(a/3). Because the local minimum of the first derivative has to lie on or below the x-axis, we can solve f'(sqrt(a/3))<0 for a and find that a>3/4

    • @NadiehFan
      @NadiehFan Před 3 hodinami

      I don't think your reasoning is correct. If the graph of the quartic intersects the x-axis at 4 distinct points (meaning we have 4 distinct real zeros) then the first derivative has _three_ distinct zeros, one in between each two consecutive zeros of the quartic. In fact, this gives yet another way to approach this problem. The condition for the first derivative to be zero is 4x³ − 4ax − 1 = 0 or x³ − ax − ¼ = 0 This is a depressed cubic x³ + px + q = 0 which has three distinct real zeros if and only if (½q)² + (⅓p)³ < 0 so a must then satisfy (−⅛)² + (−⅓a)³ < 0 which indeed gives a > ¾. This is a _necessary_ condition for the quartic x⁴ − 2ax² − x + (a² − a) to have four distinct real zeros but we would still need to prove that this is also a _sufficient_ condition. In fact we must prove that the two local minima of x⁴ − 2ax² − x + (a² − a) are both negative for a > ¾ to have four distinct real zeros and I don't see you doing that. The two zeros of the second derivative 12x² − 4a give the positions of the inflection points at x = √(a/3) and x = −√(a/3) but your claim that the point where the first derivative reaches a local minimum, that is, at x = √(a/3), has to lie on or below the x-axis makes no sense. In fact, both inflection points can lie above the x-axis and then the graph of the quartic can still cross the x-axis at four distinct points. And in fact if we substitute x = √(a/3) in f'(x) = 4x³ − 4ax − 1 and solve for f'(√(a/3)) < 0 we do _not_ get a > ¾.

    • @frankvanhertrooij5581
      @frankvanhertrooij5581 Před 2 hodinami

      @@NadiehFan Thank you for your observations. First, I agree with your point about the first derivative needing to have at least 3 zeroes for the function to have 4 distinct real roots. The reason I said there need to be at least two roots, is because I wanted to include identical roots. Your other point is more interesting, because I wrongly assumed the two local minima of the function to always be negative, which seems to be true for this particular function, but not for a general quartic. In a general case, one could remove all the real roots by adding a constant to the function, which would not be visible from the derivative. My question then becomes, what is it about the particular constant of a^2-a that ensures that the local minima are negative?

  • @kennethgee2004
    @kennethgee2004 Před 7 hodinami

    first of all you just know is not an argument. I just know because you state a reason is an argument. Like I now because i have seen this form of limit and thew general equation has a vertical asymptote and the limit from the left and right do not converge is an argument. "Just trust me bro" is not used in math and science. Funny? maybe.

    • @kennethgee2004
      @kennethgee2004 Před 7 hodinami

      but on a more serious note. this is why we should have never dropped the infinitesimal part from calculus. it would be accurate to say that as we approach the limit as x approaches 3 from the left or right that we are adding or taking away an infinitesimal. such that the equation does not need concrete examples this would show that on either side of the asymptote that the signs of the graph changes and thus do not converge. We could also look at converge tests to prove that the limit does not converge and thus is DNE.

  • @HarshKumar66743
    @HarshKumar66743 Před 7 hodinami

    16

  • @MichaelIfeco-tj1jc
    @MichaelIfeco-tj1jc Před 8 hodinami

    Please solve this "the limit as x tends to 1/3 3x-1/5x+1=0"

  • @manganeseheptoxide7825
    @manganeseheptoxide7825 Před 8 hodinami

    It is entirely possible to do without the use of lambert W. Just need to perform the same operations you did for converting -ln(√2) for converting into the W function, and then compare both sides. You end up with: ln(1/2)e^(ln(1/2)) = -ln(x)e^(-ln(x)) By comparing both sides you find: ln(1/2)=-ln(x) x=2

  • @akramhasan
    @akramhasan Před 8 hodinami

    You are best teacher in differentiation

  • @EVELYNACQUAH-cp2gw
    @EVELYNACQUAH-cp2gw Před 9 hodinami

    Please I want u to help me with a matrix question

  • @kenfrank2730
    @kenfrank2730 Před 11 hodinami

    You are a gifted instructor. But tell us about yourself. Where did you get your math background. You are a mystery man.

  • @kenfrank2730
    @kenfrank2730 Před 11 hodinami

    Very good video, and I like your t-shirt.

  • @MathCuriousity
    @MathCuriousity Před 11 hodinami

    Mind blowingly good video! Small mistake at 14:38. Denominator should be x-0. I love your videos though! Any chance you could explain why “every power series is a Taylor series” without all of the heavy analysis stuff in Borel’s proof?! I never took analysis and this “every power series is a Taylor series” is really bothering me !

  • @Jr-qo4ls
    @Jr-qo4ls Před 11 hodinami

    So well explained. If you had been my teacher in school I would’ve had a way different life.

  • @ulysslombu-dji-mabicke1868
    @ulysslombu-dji-mabicke1868 Před 12 hodinami

    You actually don't have to check all the conditions of inequality to mach. Just pick the two minor sides and add 'em then compare to the greater side.

  • @mochi-zj6pw
    @mochi-zj6pw Před 12 hodinami

    hey man your voice is so cool.....i was kinnda like dancing ....

  • @arikbrock3623
    @arikbrock3623 Před 12 hodinami

    That's not correct . X^2187 = (X^2188)/X = 1/X . The answer is -(sqr2)i

  • @abdulmoeed581
    @abdulmoeed581 Před 13 hodinami

    To the point, with perfect explanation, telling exactly what we need to know without stretching it way too long nor just doing the solutions! Subscribed

  • @saisankarujjwal330
    @saisankarujjwal330 Před 13 hodinami

    OMG amazing . Love from ♥️🇮🇳

  • @nothingbutmathproofs7150
    @nothingbutmathproofs7150 Před 14 hodinami

    I too am unclear why you think that a>-1/4 AND a>3/4. You might be correct, but can you please explain why it's not a.-1/4 OR a>3/4?

    • @PrimeNewtons
      @PrimeNewtons Před 14 hodinami

      When a variable satisfies two inequalities, it satisfies the intersection.

  • @Arinjaytayde
    @Arinjaytayde Před 15 hodinami

    16

  • @user-di1rv4jh1x
    @user-di1rv4jh1x Před 15 hodinami

    Sir I really enjoy you videos Whenever I watch your videos I Learn with enjoys❤️ Really loves your videos, you are amazing 😻

  • @Straight_Talk
    @Straight_Talk Před 15 hodinami

    Are you familiar with the discriminant (b^2 - 4ac)?

    • @PrimeNewtons
      @PrimeNewtons Před 15 hodinami

      Don't think so

    • @Straight_Talk
      @Straight_Talk Před 15 hodinami

      ​@@PrimeNewtonsIt's the part of the quadratic formula inside the square root.

  • @Sonny2009
    @Sonny2009 Před 17 hodinami

    awesome

  • @dirklutz2818
    @dirklutz2818 Před 17 hodinami

    Tremendous! What a splendid strategy to attack this problem.

  • @poucatelha1983
    @poucatelha1983 Před 17 hodinami

    This was so very helpful. Thank you!

  • @Sonny2009
    @Sonny2009 Před 19 hodinami

    One thing I get confused is Newton's f prime notation drops the dx. But Liebnez always keeps the dx. Then when we try to do integral we need to write dx back to f prime. Does anybody know why that is? And

  • @petarorevic3877
    @petarorevic3877 Před 19 hodinami

    legend

  • @eboroemmanuel5606
    @eboroemmanuel5606 Před 21 hodinou

    You teach really nice but ill suggest you give copius example to strengthen what we already know 😊 ....my cadid advise😅

  • @robertveith6383
    @robertveith6383 Před 22 hodinami

    *@ Prime Newtons* -- As with another comment in another video of yours, please *stop* using the implication symbol. The equals symbols needs to be used instead.