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AllQuestion and Answers: Page 1741

Question Number 34116 Answers: 0 Comments: 1

Question Number 34110 Answers: 0 Comments: 2

Question Number 34109 Answers: 0 Comments: 0

Question Number 34107 Answers: 0 Comments: 6

Question Number 34114 Answers: 0 Comments: 0

Question Number 34113 Answers: 0 Comments: 0

Question Number 34115 Answers: 0 Comments: 1

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.

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 ))