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Question Number 34095    Answers: 0   Comments: 0

Question Number 34094    Answers: 0   Comments: 2

Question Number 34092    Answers: 2   Comments: 9

l_n i_ m_∞ ((((n!))/((nm)^n )))^(1/n)

$$\underset{{n}} {{l}}\underset{} {{i}}\underset{\infty} {{m}}\:\left(\frac{\left({n}!\right)}{\left({nm}\right)^{{n}} }\right)^{\frac{\mathrm{1}}{{n}}} \\ $$

Question Number 34098    Answers: 0   Comments: 13

Since the beginning several persons with their experties had left the forum... Newcommers don′t know them,but they can explore the past of the forum and recognise their precious work! Think the forum as cricket. Some were ′bowlers′ and others were ′batsmen′. Bowlers: questioners and batsmen: answerers. In my period(When I was somewhat more active) some good ′bowlers′ were sanusihammed,tawakalitu,tawa.Some good ′batsmen′ were prakash jain, Yozzi. 123556 was ′all rounder′.An other energetic ′all-rounder player′ was filups. ′Bowlers′ also play vital role... ... Speaking of present period. Recently our ′Captain′ has left the forum.An expert,an honest and a hardworker ′player′ and leader. Also a good ′bowler′ of the present period has left us. I request mrW and Mr tinkutara to come back please! The forum needs you! Also request Ajeet bhaya(a lovely name of Mr Ajfour) to become more active.He is, like mrW, an important figure. Request by a 12th player.

$$\mathrm{Since}\:\mathrm{the}\:\mathrm{beginning}\: \\ $$$$\mathrm{several}\:\mathrm{persons}\:\mathrm{with}\:\mathrm{their}\:\mathrm{experties} \\ $$$$\mathrm{had}\:\mathrm{left}\:\mathrm{the}\:\mathrm{forum}... \\ $$$$\mathrm{Newcommers}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{them},\mathrm{but} \\ $$$$\mathrm{they}\:\mathrm{can}\:\mathrm{explore}\:\mathrm{the}\:\mathrm{past}\:\mathrm{of}\:\mathrm{the}\:\mathrm{forum} \\ $$$$\mathrm{and}\:\mathrm{recognise}\:\mathrm{their}\:\mathrm{precious}\:\mathrm{work}! \\ $$$$\mathrm{Think}\:\mathrm{the}\:\mathrm{forum}\:\mathrm{as}\:\mathrm{cricket}. \\ $$$$\mathrm{Some}\:\mathrm{were}\:'\mathrm{bowlers}'\:\mathrm{and}\:\mathrm{others}\:\mathrm{were} \\ $$$$'\mathrm{batsmen}'.\:\mathrm{Bowlers}:\:\mathrm{questioners}\:\:\mathrm{and} \\ $$$$\mathrm{batsmen}:\:\mathrm{answerers}. \\ $$$$\mathrm{In}\:\mathrm{my}\:\mathrm{period}\left(\mathrm{When}\:\mathrm{I}\:\mathrm{was}\:\mathrm{somewhat}\right. \\ $$$$\left.\mathrm{more}\:\mathrm{active}\right)\:\mathrm{some}\:\mathrm{good}\:'\mathrm{bowlers}'\:\mathrm{were} \\ $$$$\boldsymbol{\mathrm{sanusihammed}},\boldsymbol{\mathrm{tawakalitu}},\boldsymbol{\mathrm{tawa}}.\mathrm{Some} \\ $$$$\mathrm{good}\:'\mathrm{batsmen}'\:\mathrm{were}\:\boldsymbol{\mathrm{prakash}}\:\boldsymbol{\mathrm{jain}}, \\ $$$$\boldsymbol{\mathrm{Yozzi}}.\:\mathrm{123556}\:\mathrm{was}\:'\mathrm{all}\:\mathrm{rounder}'.\mathrm{An}\:\mathrm{other} \\ $$$$\mathrm{energetic}\:\:'\mathrm{all}-\mathrm{rounder}\:\mathrm{player}'\:\mathrm{was}\:\boldsymbol{\mathrm{filups}}. \\ $$$$'\mathrm{Bowlers}'\:\mathrm{also}\:\mathrm{play}\:\mathrm{vital}\:\mathrm{role}... \\ $$$$... \\ $$$$\mathrm{Speaking}\:\mathrm{of}\:\mathrm{present}\:\mathrm{period}. \\ $$$$\mathrm{Recently}\:\mathrm{our}\:'\mathrm{Captain}'\:\mathrm{has}\:\mathrm{left}\:\mathrm{the} \\ $$$$\mathrm{forum}.\mathrm{An}\:\boldsymbol{\mathrm{expert}},\mathrm{an}\:\boldsymbol{\mathrm{honest}}\:\mathrm{and}\:\mathrm{a} \\ $$$$\boldsymbol{\mathrm{hardworker}}\:\:'\mathrm{player}'\:\mathrm{and}\:\mathrm{leader}.\: \\ $$$$\mathrm{Also}\:\mathrm{a}\:\mathrm{good}\:'\mathrm{bowler}'\:\mathrm{of}\:\mathrm{the}\:\mathrm{present} \\ $$$$\mathrm{period}\:\mathrm{has}\:\mathrm{left}\:\mathrm{us}. \\ $$$$\mathrm{I}\:\mathrm{request}\:\boldsymbol{\mathrm{mrW}}\:\mathrm{and}\:\boldsymbol{\mathrm{Mr}}\:\boldsymbol{\mathrm{tinkutara}} \\ $$$$\mathrm{to}\:\mathrm{come}\:\mathrm{back}\:\mathrm{please}!\:\mathrm{The}\:\mathrm{forum} \\ $$$$\boldsymbol{\mathrm{needs}}\:\mathrm{you}! \\ $$$$\mathrm{Also}\:\mathrm{request}\:{Ajeet}\:{bhaya}\left(\mathrm{a}\:\mathrm{lovely}\right. \\ $$$$\left.\mathrm{name}\:\mathrm{of}\:\boldsymbol{\mathrm{Mr}}\:\boldsymbol{\mathrm{Ajfour}}\right)\:\mathrm{to}\:\mathrm{become}\:\mathrm{more} \\ $$$$\mathrm{active}.\mathrm{He}\:\mathrm{is},\:\mathrm{like}\:\mathrm{mrW},\:\mathrm{an}\:\mathrm{important} \\ $$$$\mathrm{figure}. \\ $$$$\mathrm{Request}\:\mathrm{by}\:\mathrm{a}\:\mathrm{12th}\:\mathrm{player}. \\ $$

Question Number 34081    Answers: 1   Comments: 0

2^n −2^(n−1) =4 .find n^(n.)

$$\mathrm{2}^{{n}} −\mathrm{2}^{{n}−\mathrm{1}} =\mathrm{4}\:.{find}\:{n}^{{n}.} \\ $$

Question Number 34066    Answers: 1   Comments: 0

show that− sin 10−(√3)sec10=4.

$$\mathrm{show}\:\mathrm{that}− \\ $$$$\mathrm{sin}\:\mathrm{10}−\sqrt{\mathrm{3}}\mathrm{sec10}=\mathrm{4}. \\ $$

Question Number 34064    Answers: 1   Comments: 0

Question Number 34056    Answers: 2   Comments: 3

x^(3z) =1 x^2 =y z=y^n FIND THE VALUE OF n please i need your help ASAP. thanks

$${x}^{\mathrm{3}{z}} =\mathrm{1}\: \\ $$$${x}^{\mathrm{2}} ={y} \\ $$$${z}={y}^{{n}} \\ $$$${FIND}\:{THE}\:{VALUE}\:{OF}\:{n} \\ $$$${please}\:{i}\:{need}\:{your}\:{help}\:{ASAP}.\:{thanks} \\ $$

Question Number 34051    Answers: 1   Comments: 0

2dy/dx+y=0 y(0)=−3

$$\mathrm{2}{dy}/{dx}+{y}=\mathrm{0}\:\:{y}\left(\mathrm{0}\right)=−\mathrm{3} \\ $$

Question Number 34044    Answers: 2   Comments: 2

what is the remainder when (111..)+(222..)+(333..)+....+(77..) is divided by 37

$${what}\:{is}\:{the}\:{remainder}\:{when}\: \\ $$$$\left(\mathrm{111}..\right)+\left(\mathrm{222}..\right)+\left(\mathrm{333}..\right)+....+\left(\mathrm{77}..\right) \\ $$$${is}\:{divided}\:{by}\:\mathrm{37} \\ $$

Question Number 34063    Answers: 1   Comments: 3

Let A= { 1,2,3,4 } . Number of functions f:A→A satisfying f(f(x))=x ∀x∈A, is ?

$$\boldsymbol{\mathrm{L}}\mathrm{et}\:\mathrm{A}=\:\left\{\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\:\right\}\:.\:\mathrm{N}{umber}\:\mathrm{of}\:\mathrm{functions} \\ $$$$\mathrm{f}:\mathrm{A}\rightarrow{A}\:\mathrm{satisfying}\:\mathrm{f}\left(\mathrm{f}\left({x}\right)\right)={x}\:\forall{x}\in\mathrm{A},\:\mathrm{is}\:? \\ $$

Question Number 34031    Answers: 0   Comments: 0

Prove that for every positive real numbers x, y, z and xyz = 1, hold (x + y + z)^2 ((1/x^2 ) + (1/y^2 ) + (1/z^2 )) ≥ 9 + 2(x^3 + y^3 + z^3 ) + 4((1/x^3 ) + (1/y^3 ) + (1/z^3 ))

$${Prove}\:\:{that}\:\:{for}\:\:{every}\:\:{positive}\:\:{real}\:\:{numbers}\:\:{x},\:{y},\:{z}\:\:{and}\:\:\:{xyz}\:\:=\:\:\mathrm{1},\:\:{hold} \\ $$$$\left({x}\:+\:{y}\:+\:{z}\right)^{\mathrm{2}} \left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{y}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{z}^{\mathrm{2}} }\right)\:\:\geqslant\:\:\mathrm{9}\:+\:\mathrm{2}\left({x}^{\mathrm{3}} \:+\:{y}^{\mathrm{3}} \:+\:{z}^{\mathrm{3}} \right)\:+\:\mathrm{4}\left(\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{{y}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{{z}^{\mathrm{3}} }\right)\: \\ $$

Question Number 34029    Answers: 1   Comments: 1

Number of integral values of x for which ((((π/2^(tan^(−1) x) )−4)(x−4)(x−10))/(x! − (x−1)!)) < 0

$$\boldsymbol{{N}}{umber}\:{of}\:{integral}\:{values}\:{of}\:{x}\:{for} \\ $$$${which}\: \\ $$$$\frac{\left(\frac{\pi}{\mathrm{2}^{\mathrm{tan}^{−\mathrm{1}} {x}} }−\mathrm{4}\right)\left({x}−\mathrm{4}\right)\left({x}−\mathrm{10}\right)}{{x}!\:−\:\left({x}−\mathrm{1}\right)!}\:<\:\mathrm{0} \\ $$

Question Number 34021    Answers: 1   Comments: 2

find the value of ∫_0 ^(+∞) ((cos(αx))/((x^2 +1)( x^2 +2)(x^2 +3)))dx 2) calculate ∫_0 ^∞ (dx/((x^2 +1)(x^2 +2)(x^2 +3)))

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{cos}\left(\alpha{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left(\:{x}^{\mathrm{2}} +\mathrm{2}\right)\left({x}^{\mathrm{2}} +\mathrm{3}\right)}{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{2}\right)\left({x}^{\mathrm{2}} +\mathrm{3}\right)} \\ $$

Question Number 34020    Answers: 0   Comments: 1

let p(x)=cos(2n arccos(x)) with x∈[−1,1] find the roots of p(x) and factorize p(x)

$${let}\:{p}\left({x}\right)={cos}\left(\mathrm{2}{n}\:{arccos}\left({x}\right)\right)\:\:{with}\:{x}\in\left[−\mathrm{1},\mathrm{1}\right] \\ $$$${find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right)\:{and}\:{factorize}\:\:{p}\left({x}\right) \\ $$

Question Number 34019    Answers: 0   Comments: 4

n integr decompose imsidr R[x] the fraction F(x) = (1/((x^2 −1)^n ))

$${n}\:{integr}\:{decompose}\:{imsidr}\:{R}\left[{x}\right]\:{the}\:{fraction} \\ $$$${F}\left({x}\right)\:=\:\:\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} \:−\mathrm{1}\right)^{{n}} } \\ $$

Question Number 34013    Answers: 0   Comments: 0

find Σ_(n=0) ^∞ ((cos((2n+1)(π/4)))/((2n+1)^2 )) .

$${find}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left(\left(\mathrm{2}{n}+\mathrm{1}\right)\frac{\pi}{\mathrm{4}}\right)}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }\:. \\ $$

Question Number 34011    Answers: 0   Comments: 0

calculate Σ_(n=1) ^∞ ((cos(nx))/n^2 ) and Σ_(n=1) ^∞ ((sin(nx))/n^2 )

$${calculate}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{cos}\left({nx}\right)}{{n}^{\mathrm{2}} }\:\:{and}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{sin}\left({nx}\right)}{{n}^{\mathrm{2}} } \\ $$

Question Number 34007    Answers: 1   Comments: 0

lim_(x→2) (((√(x−2)) +(√x) −(√2))/(√(x^2 −4))) is ?

$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\sqrt{{x}−\mathrm{2}}\:+\sqrt{{x}}\:−\sqrt{\mathrm{2}}}{\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}}\:\:{is}\:? \\ $$

Question Number 34005    Answers: 1   Comments: 4

((4k+1)/(k+3)),(4k+1,k+3)=(11,k+3)=1or11; I can′t understand.Who can help me?

$$\frac{\mathrm{4}{k}+\mathrm{1}}{{k}+\mathrm{3}},\left(\mathrm{4}{k}+\mathrm{1},{k}+\mathrm{3}\right)=\left(\mathrm{11},{k}+\mathrm{3}\right)=\mathrm{1}{or}\mathrm{11}; \\ $$$${I}\:{can}'{t}\:{understand}.{Who}\:{can}\:{help}\:{me}? \\ $$

Question Number 33997    Answers: 1   Comments: 0

If the range of the function f(x) = ((x−1)/(p−x^2 +1)) does not contain any values belonging to the interval [−1,((−1)/3)] then true set of values of p is ?

$$\boldsymbol{{I}}\mathrm{f}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\: \\ $$$$\mathrm{f}\left({x}\right)\:=\:\frac{{x}−\mathrm{1}}{\mathrm{p}−{x}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{does}\:\mathrm{not}\:\mathrm{contain}\:\mathrm{any} \\ $$$$\mathrm{values}\:\mathrm{belonging}\:\mathrm{to}\:\mathrm{the}\:\mathrm{interval} \\ $$$$\left[−\mathrm{1},\frac{−\mathrm{1}}{\mathrm{3}}\right]\:{then}\:{true}\:{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\mathrm{p}\:\mathrm{is}\:? \\ $$

Question Number 33990    Answers: 0   Comments: 1

let give I =∫_0 ^1 ln(x)ln(1+x)dx give I at form of serie .

$${let}\:{give}\:{I}\:\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{1}+{x}\right){dx}\: \\ $$$${give}\:{I}\:{at}\:{form}\:{of}\:{serie}\:. \\ $$

Question Number 33989    Answers: 0   Comments: 0

let f(x)= (e^(−x) /(cosx)) , 2π periodic even developp f at fourier serie .

$${let}\:{f}\left({x}\right)=\:\frac{{e}^{−{x}} }{{cosx}}\:\:\:\:,\:\mathrm{2}\pi\:{periodic}\:{even} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}\:. \\ $$

Question Number 33988    Answers: 1   Comments: 0

give the algebric form of (1+i)^i .

$${give}\:{the}\:{algebric}\:{form}\:{of}\:\left(\mathrm{1}+{i}\right)^{{i}} . \\ $$

Question Number 33987    Answers: 0   Comments: 2

find ∫_(−∞) ^(+∞) ((cos(αx))/((1+x^2 )^3 )) dx with α≥0 .

$${find}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left(\alpha{x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:{dx}\:{with}\:\alpha\geqslant\mathrm{0}\:. \\ $$

Question Number 33986    Answers: 0   Comments: 1

find ∫_(−∞) ^(+∞) ((cos(tx))/((1+x^2 )^2 )) dx with t≥0

$${find}\:\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left({tx}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:{with}\:{t}\geqslant\mathrm{0} \\ $$

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