Calculusfx's Posts
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 Education › Re: Nairaland Mathematics Clinic by Calculusfx: 9:43pm On Nov 20, 2013 |
benbuks: Find the anti-derivative of (cosx +1)^-2...which makes it integral.1/(cosx+1)^2 first,make tan(x/2)=t(for those of linear trig but for quadratic,u use tanx=t)from triangle and pythagora's theorem,u will get sin(x/2)=t/sqrt(1+t^2) and cos(x/2)=1/sqrt(1+t^2)...and from half-angle formula,sinx=2sin(x/2)cos(x/2)=2t/(1+t^2)...and cosx=cos^2(x/2)-sin^2(x/2)=(1-t^2)/(1+t^2)...from there,don't forget tan(x/2)=t...find d/dx of both sides...(1/2)sec^2(x/2)dx=dt...therefore dx=2cos^2(x/2)dt=2dt/(1+t^2)...with all with have got...dx=2dt/(1+t^2)...cosx=(1-t^2)/(1+t^2)...let's forget sinx cos we don't need it here but don't forget that tan(x/2)=t...so,back to the question,integral 1dx/(cosx+1)^2...let's first do cosx+1 before coming to the integral...and don't forget the value of our cosx...so that cosx+1=2/(1+t^2)...(i)...from question...we were asked to solve.1/(cosx+1)^2...so inverse of (i) gives (1+t^2)^2/4...so the integral function now become...integral (1+t^2)^2/4 *dx...substitute dx=2dt/(1+t^2)...so,it will become (1/2)integral(1+t^2)dt...=...(1/2){t+(t^3)/3}+c...don't forget tan(x/2)=t...then 1/2{tan(x/2)+tan^3(x/2)/3}+c... |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 10:24pm On Nov 19, 2013 |
[quote author=ameer!]Prove dat cosecX-1/cosecX+1=[1-tan(x/2)/1+tan(x/2)]^2. . .any1 dat cn prove dis will have a special reward.I promise.[/quote]...hmmm.from rhs {(1-tan(1/2)x)/(1+tan(1/2)x)}^2 since tan(1/2)x=sin(1/2)x/cos(1/2)x...then {[1-sin(1/2)x/cos(1/2)x]/{1+sin(1/2)x/cos(1/2)x}^2...{LET'S DEAL WITH THE ONE IN THE BRACKET FIRST)multiply the numerator and denominator by cos(1/2)x which gives {(cos(1/2)x-sin(1/2)x)/(cos(1/2)x+sin(1/2)x)}^2...then square to give (sin^2(1/2)x-2sin(1/2)xcos(1/2)x+cos^2(1/2)x)/(sin^2(1/2)x+2sin(1/2)xcos(1/2)x+cos^2(1/2)x)...don't forget from trig. that cos^2(1/2)x+sin^2(1/2)x=1 and 2sin(1/2)xcos(1/2)x=sinx...substitute those to give...(1-sinx)/(1+sinx)...multiply the numerator and the denominator by 1/sinx...to give {1/sinx(1-sinx)/1/sinx(1+sinx)=(1/sinx-1)/(1/sinx+1)...don't forget 1/sinx=cosecx...substitute that to give cosecx-1/cosecx+1 QED |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 10:21pm On Nov 19, 2013 |
I have not been to the thread since morning...kudos to master laplacian,master echibuzor,master factorial(who used logic to abuse me on the quiz thread),my main oga rhydex,master chiboy and master smurfy...for not allowing the clinic to be silent as mortuary...i respect you all. 1 Like |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 10:13pm On Nov 19, 2013 |
Hmmmm |
| Education › Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Calculusfx: 3:17pm On Nov 18, 2013 |
General richiez...well done.you are really doing great |
| Education › Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Calculusfx: 12:10pm On Nov 17, 2013 |
factorial1: Cool n' straight 4ward, bravo!laughs,i know little things about logic bro,thanx 1 Like |
| Education › Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Calculusfx: 9:14pm On Nov 16, 2013 |
I guess no master professor ortarico Ortarico: Correct!how did you turn 5 to 30 and where is the y with 5(you have slaughtered it) aysuccess99: This is the solution:,i think this is a way of doing it,from the question 6x^2+7xy-5,comparing it with general quadratic formula,ax^2+bx+c and since a is not equal to 1,then you multiply a by c(6*-5=-30),then find 2 numbers you will multiply that will give you -30 and added to give +7...let's do it like this...you know + * -=- and - * +=-,i could remember secondary school life that when it resembles,it's + and when it doesn't resemble it's - that's the reason why +*+=+ and -*-=+,so let's continue...then you find the factors of 30 you know,but don't forget it's -30 ooo,and +*- or -*+ can work for it...the factors are 1 and 30,2 and 15,3 and 10.i think that's all,no,we still have 5 and 6...so checking those those factors,which one can be subtracted or added to give 7,can you guess?no no no,it's 3 and 10 and we are using + and - or - and +...then we use both [+3 and -10=-7...-3 and +10=+7(on addition)]...and we need +7 so we take what?Good, -3 and +10...let's pause for now and let me take a bottle of water.... ....so,we have had enough rest,let's continue,then we substitute it to where we see +7 from 6x^2+7xy-5y^2,then 6x^2-3xy+10xy-5y^2...from the first two factorize 3x to give 3x(2x-y)+5y(2x-y),since 2x-y is common to both,factorize to give (2x-y)(3x+5y)...hope you understand? |
| Education › Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Calculusfx: 9:14pm On Nov 16, 2013 |
Hmmmm |
| Education › Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Calculusfx: 8:33pm On Nov 16, 2013 |
Ortarico: Correct! |
| Music/Radio › Re: What Are The Songs You Never Get Tired Of?? by Calculusfx: 4:23pm On Nov 16, 2013 |
Songs of the saints by fimba onyeka any don moen song...but i love sing for joy,we come to bless ur name,be where you are,etc... any women of faith song. Peter buchi-it's well,Jesus must be honoured and nma nma. Any Westlife's song |
| Education › Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx(op): 10:21am On Nov 15, 2013 |
To square anything which comes between 90-100...e.g 96...say 100-96=4...subtract the 4 from 96 to give 92,square the 4 to give 16,write it together to give 9216 |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 10:16am On Nov 15, 2013 |
jackpot: you are wrong, sweetheart |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 10:14am On Nov 15, 2013 |
Mbahchiboy: dephth=25m(d last distance d snail must reach). factorial1: Nice one bro, it can also be done as this, since the snail would clime 2.0m up and slide down 1.5m, d total distance it will cover per day will be (2-1.5)m=0.5m, therefore the days dah'll take the snail to come out of the well= Depth/total distance covered per day which is equal to 25m/0.5m=50days. Mbahchiboy: dephth=25m(d last distance d snail must reach).i agree with master jackpot on the question |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 7:56am On Nov 15, 2013 |
LogoDWhiz: How can 0.9999...=1?.from sum to infinity....s=a/(1-r).from the question a=0.9 and r=0.1.substitute those to get s=0.9/(1-0.1)=0.9/0.9 then s=1 1 Like |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 1:13pm On Nov 14, 2013 |
Laplacian: ...the indomitable f(x)...nice wrk....i respect you master,though only the deep can come into the deep.hmmm,i pray i find myself in maths world like you o...thanx for the compliment sir |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 12:51pm On Nov 14, 2013 |
Laplacian: ...sin2x+sinx=1...find x....hmmm,here is my own approach to it...sin2x+sinx=1...2sinxcosx+sinx=1...2sinx.sqrt(1-sin^2x)+sinx=1...{let sinx be a...(i)}...2a.sqrt(1-a^2)+a=1...2a.sqrt(1-a^2)=1-a...square both sides...4a^2(1-a^2)=1-2a+a^2...4a^2-4a^4=1-2a+a^2...4a^4-3a^2-2a+1=0,it's obvious that a=1(one of the four roots) then we divide 4a^4-3a^2-2a+1 by a-1 to give 4a^3+4a^2+a-1=0...then transform the equation to reduced cubic equation to get by representing a as y-1/3...(ii) to give y^3-y/12-7/27...you can use any method for solving cubic polynomial to do it but for me,i used tartaglia's method for finding real root of a cubic equation and got y as 0.68114(approximated),don't forget that a=y-1/3 and by substituting that a=0.34781(the first root of the cubic polynomial)...to get the other two roots...from relationship between the co-efficients and roots of a polynomial...a1+a2+a3=-1 a1.a2.a3=0.25(from the polynomial 4a^3+4a^2+a-1=0)...let a1 be 0.34781,by solving a2+a3=-1.34781 and a2.a3=0.7188 and by solving the simultaneous equation a={-1.34781±j1.0287}/2...with all we have done so far,the two real roots got were a=1 and a=0.34781,don't forget that sinx=a...let a be 1,then sinx=1 and x=90 and if a=0.34781,sinx=0.34781 and x=20.35...i rest my case 1 Like |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 10:30am On Nov 14, 2013 |
benbuks: 0.977777. . .where ... Represents continuity to infinity.0.9+0.0777...then take 0.0777...and let's work on it.0.07...*10-0.07...=0.77...-0.07...then 0.07(10-1)=0.7 then 0.07=0.7/9 which is equal to 7/90 and don't forget we had 0.9+0.07... same as 9/10+7/90 which now equals to 44/45...i rest my case |
| Education › Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx(op): 9:05am On Nov 14, 2013 |
To square anything which comes between 51-60...say 57...the unit is 7...add the 7 to 25 to give 32...keep that and square that 7 to give 49..write it together to give 3249... 2 Likes |
| Education › Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx(op): 9:02am On Nov 14, 2013 |
Laplacian: nice work bro...its a special case of what i showed earlier...here's a simple proof;.you are one of my ogas bro.so,i can't quote you wrong.but there are still better and faster ways i've got of calculating faster and easier than that.you can even calculate some faster than someone with calculator(believe me,i'm not joking o)...let's play with one more for this morning.here we go...... |
| Education › Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx(op): 1:14am On Nov 14, 2013 |
doubleDx: Nice one generals, I greet y'all!...master,i respect sir,welcome to the thread... |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 11:49pm On Nov 13, 2013*. Modified: 12:07am On Nov 14, 2013 |
benbuks: the sum of the first two terms of a g.p is x and the sum of last two terms is y .If there are n terms..the first two terms are a and ar,the last two terms are ar^(n-2)+ar^(n-1)...from the question a+ar=x...(i) and ar^(n-2)+ar^(n-1)=y...(ii).from (ii)factorize r^(n-2) to give r^(n-2){a+ar}=y...(iii).divide iii by 1 to give r^(n-2)=y/x...then r={y/x}^{1/(n-2)} |
| Education › Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx(op): 11:34pm On Nov 13, 2013 |
To square anything which comes between 25-50...say 46...just say 46 minus 25...to give 21,keep that,say 50 minus 46 to give 4(square the 4 to give 16)...take the 16 to 21 and write together...so that answer for 46^2 is 2116...just other ones and ask me questions on the ones that seems to be difficult between 25-50...but note this,it works for all numbers in that range... 1 Like |
| Education › Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx(op): 11:31pm On Nov 13, 2013 |
Great...kudos to everybody in the house |
| Education › Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Calculusfx: 9:28pm On Nov 12, 2013 |
The thread is very interesting,i'm sure we gonna rock it together tomorrow...i respect you people.i promise to send my own questions tomorrow@sir richiez.. |
| Education › Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Calculusfx: 10:19am On Nov 12, 2013 |
Greetings to all the generals in the house |
| Education › Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx(op): 7:33am On Nov 12, 2013 |
Anybody in the house? |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 12:47am On Nov 12, 2013 |
Alpha Maximus: @Calculusf(x) , I've seen , studied and learnt from your work here on this thread and you have proven your worth and skill with numbers time and time again with unique approaches and also that your characteristic humility.Godspeed to your ill acquaintance though and I wish him/her a speedy recovery..thank you my brother,i respect you mathematical approaches to question,you are great bro.and try to be greater[quote author= d citizen]@calculus It is a good thing dat u are back. I wish ur loved one a speedy recovery. Keep the math clinic running with ur great and incisive contribution. Take heart and get urself together again[/quote]...thank you very much my master,i'm very grateful. |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 12:44am On Nov 12, 2013 |
Hmmmm |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 12:41am On Nov 12, 2013 |
[quote author=Alpha Maximus][/quote]@olarewaju's question on the expansion of (a+b+c)(a+b-c)(a-b+c)(-a+b+c)...re-arrange to give (a+b+c)(a+b-c){c+(a-b)}{c-(a-b)}...check the ones that formes difference of two squares there...then {(a+b)^2-c^2}{c^2-(a-b)^2}...expand to give {a^2+b^2+2ab-c^2}{c^2-(a^2+b^2-2ab}...then,{a^2+b^2+2ab-c^2}{c^2-a^2-b^2+2ab}...when you multiply by -1 and you make it affect the second bracket{a^2+b^2+2ab-c^2}{-c^2+a^2+b^2-2ab}...re-arrange to give {a^2+b^2+2ab-c^2}{a^2+b^2-2ab-c^2}...{a^2+b^2-c^2+2ab}{a^2+b^2-c^2-2ab}...which is another difference of two squares...{[a^2+b^2-c^2]^2-[2ab]^2}...then expand the last to give a^4+b^4+c^4-2a^2b^2-2a^2c^2-2b^2c^2 |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 12:10am On Nov 12, 2013 |
[quote author= d citizen]@jackpot, Pls donot institute a case against me. Am jst being curious about ur true identity and making a honest and passionate appeal. I have gone tru ur incisive post on this forum but at different sections especially joke and romance and i saw a smooth oscillation of ur identity from ferminism to masculinity. I really admire ur math insight and prowess .i must admit that you have a deep seated passion for math. I can see that tru ur indepth scruitiny of the working of math problems by fellow math generals in the house and i am interested in knowing ur true identity. Great female mathematicians are few but they come once in a century. I am putting you on a hotseat and challenge u to review ur identity now. I want my conscience to be clear when referring to ur gender with pronouns "he" or "she". I must salute ur courage, personal drive and sheer determination as you journey into the math world. honest n unbaised msg from the five star general.[/quote]...we are thinking the same master |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 12:06am On Nov 12, 2013 |
Ortarico: Wow, it's Innovative!hmmmm |
| Education › Re: Nairaland Mathematics Clinic by Calculusfx: 12:04am On Nov 12, 2013 |
I'm sorry.i have not been typing for quite a long time,it's just that someone whose life i cherish than mine is sick,so i don't have much time nowadays,i'm very sorry....thanx to master ortarico for remembering calculusf(x) on nairaland maths clinic...and i also greet all generals in the house starting from master richiez,double dx,and my greatest oga here who's the five star maths general(i think everybody knows him with that) master d citizen(who's the only general in the same field with me here),master 2nioshine,master jackpot...and my other generals,starting from master laplace,master alpha maximus,my brother who's also my master(ridex),master labodinho and my great pals who are my masters....benbuks and ortarico....I RESPECT YOU ALL...let's keep the thread rolling... 2 Likes |
bt pls first arrange accordn 2 lyk terms)