Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1819

Question Number 27604    Answers: 0   Comments: 1

Let S_n =(1/1^3 ) + ((1+2)/(1^3 +2^3 )) +...+((1+2+...+n)/(1^3 +2^3 +...+n^3 )); n=1,2,3,.. Then S_n is greater than

$$\mathrm{Let}\: \\ $$$${S}_{{n}} =\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}+\mathrm{2}}{\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} }\:+...+\frac{\mathrm{1}+\mathrm{2}+...+{n}}{\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +...+{n}^{\mathrm{3}} };\:{n}=\mathrm{1},\mathrm{2},\mathrm{3},.. \\ $$$$\mathrm{Then}\:{S}_{{n}} \:\mathrm{is}\:\mathrm{greater}\:\mathrm{than} \\ $$

Question Number 27601    Answers: 0   Comments: 0

f fonction numerical increasing on ]0,1] and ∫_0 ^1 f(t)dt converges prove that lim_(n−>∝) (1/n) Σ_(k=1) ^n f((k/n)) = ∫_0 ^1 f(t)dt .

$$\left.{f}\left.\:{fonction}\:{numerical}\:{increasing}\:{on}\:\right]\mathrm{0},\mathrm{1}\right]\:{and} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({t}\right){dt}\:{converges}\:{prove}\:{that}\:\:{lim}_{{n}−>\propto} \:\:\frac{\mathrm{1}}{{n}}\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{f}\left(\frac{{k}}{{n}}\right) \\ $$$$=\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({t}\right){dt}\:\:. \\ $$

Question Number 27600    Answers: 0   Comments: 1

find ∫_0 ^π (t/(2+sint)) dt

$${find}\:\:\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{t}}{\mathrm{2}+{sint}}\:{dt} \\ $$

Question Number 27599    Answers: 0   Comments: 0

let give the equation x^6 −x−1=0 by using Newton methodfind the approximate value of the real?root for this equation.

$${let}\:{give}\:{the}\:{equation}\:\:{x}^{\mathrm{6}} −{x}−\mathrm{1}=\mathrm{0}\:\:{by}\:{using}\:{Newton}\:{methodfind} \\ $$$${the}\:{approximate}\:{value}\:{of}\:{the}\:{real}?{root}\:\:{for}\:{this}\:{equation}. \\ $$

Question Number 27598    Answers: 0   Comments: 1

find ∫∫∫_D (x^2 +y^2 )dxdxy with D={x,y,z)∈R^3 /x^2 +y^2 +z^2 ≤1 and z≥0 }

$${find}\:\int\int\int_{{D}} \left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dxdxy}\:\:\:{with} \\ $$$$\left.{D}=\left\{{x},{y},{z}\right)\in{R}^{\mathrm{3}} \:\:\:/{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:\leqslant\mathrm{1}\:\:{and}\:{z}\geqslant\mathrm{0}\:\right\} \\ $$

Question Number 27597    Answers: 0   Comments: 0

find ∫ ((√(cos(2x)))/(cosx)) dx.

$${find}\:\int\:\:\frac{\sqrt{{cos}\left(\mathrm{2}{x}\right)}}{{cosx}}\:{dx}. \\ $$

Question Number 27596    Answers: 0   Comments: 1

find ∫ ^3 (√( x^2 −x^3 )) dx

$${find}\:\:\int\:\:\:^{\mathrm{3}} \sqrt{\:{x}^{\mathrm{2}} −{x}^{\mathrm{3}} }\:\:{dx} \\ $$

Question Number 27595    Answers: 0   Comments: 1

find ∫∫_D xy(√( x^2 +y^2 )) dxdy with D={ (x,y)∈R^2 / x^2 +2y^2 ≤1 ,x≥0 ,y ≥0}

$${find}\:\:\int\int_{{D}} \:\:{xy}\sqrt{\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:\:{dxdy}\:\:\:{with} \\ $$$${D}=\left\{\:\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \:+\mathrm{2}{y}^{\mathrm{2}} \:\leqslant\mathrm{1}\:\:,{x}\geqslant\mathrm{0}\:,{y}\:\geqslant\mathrm{0}\right\} \\ $$

Question Number 27603    Answers: 0   Comments: 1

Find the value of i^i ?

$${Find}\:\:{the}\:{value}\:{of}\:\:\:{i}^{{i}} \:\:? \\ $$$$ \\ $$$$ \\ $$

Question Number 27587    Answers: 1   Comments: 1

divide 12x(8x−20) by 4(2x−5)

$$\mathrm{divide}\:\mathrm{12x}\left(\mathrm{8x}−\mathrm{20}\right)\:\mathrm{by}\:\mathrm{4}\left(\mathrm{2x}−\mathrm{5}\right) \\ $$

Question Number 27581    Answers: 1   Comments: 0

If f(x)=∫(4x−x^2 )dx f(3)=22, find f(x)

$$\mathrm{If}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\int\left(\mathrm{4}\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)\boldsymbol{\mathrm{dx}} \\ $$$$\mathrm{f}\left(\mathrm{3}\right)=\mathrm{22},\:\mathrm{find}\:{f}\left(\mathrm{x}\right) \\ $$

Question Number 27580    Answers: 1   Comments: 0

Simplify (1/(1−cos a)) + (1/(1+cos a)) and leave the answer in the form⇒ sin a

$$\mathrm{Simplify}\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{cos}\:\mathrm{a}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cos}\:\mathrm{a}} \\ $$$$\mathrm{and}\:\mathrm{leave}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{form}\Rightarrow\:\:\:\mathrm{sin}\:\mathrm{a} \\ $$

Question Number 27579    Answers: 1   Comments: 0

A circle with center (−3,1) passes through the point (3,1). Find it′s equation

$$\mathrm{A}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{center}\:\left(−\mathrm{3},\mathrm{1}\right) \\ $$$$\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\: \\ $$$$\left(\mathrm{3},\mathrm{1}\right).\:\mathrm{Find}\:\mathrm{it}'\mathrm{s}\:\mathrm{equation} \\ $$

Question Number 27578    Answers: 0   Comments: 1

if f(x)=((2x−3)/((x^2 −1)(x+2))) 1. Find the value for which f(x) is undefied. 2.Express f(x) in partial fraction

$$\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{2x}−\mathrm{3}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{x}+\mathrm{2}\right)} \\ $$$$\mathrm{1}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{for}\:\mathrm{which}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{undefied}. \\ $$$$\mathrm{2}.\mathrm{Express}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fraction} \\ $$

Question Number 27577    Answers: 0   Comments: 0

find the equation of the line of the stationary point y=x^2 (x−3) and the distance between them

$$\mathrm{find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{stationary}\:\mathrm{point}\: \\ $$$$\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{x}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{x}}−\mathrm{3}\right)\: \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{them} \\ $$

Question Number 27594    Answers: 0   Comments: 1

solve the differencial equation (1−x^2 )y^′ −xy =1 .

$${solve}\:{the}\:\:{differencial}\:{equation} \\ $$$$\left(\mathrm{1}−{x}^{\mathrm{2}} \right){y}^{'} \:−{xy}\:=\mathrm{1}\:\:\:. \\ $$

Question Number 27568    Answers: 1   Comments: 0

carol is 6 times as old as her nephew Hondo.Baby is 22 years yonger than her aunt carol.In four years carol′s age will be twice the sum of Hondo′s and Baby′s age.How old is each perso n now?

$${carol}\:{is}\:\mathrm{6}\:{times}\:{as}\:{old}\:{as}\:{her}\:{nephew} \\ $$$${Hondo}.{Baby}\:{is}\:\mathrm{22}\:{years}\:{yonger}\:{than} \\ $$$${her}\:{aunt}\:{carol}.{In}\:{four}\:{years}\:{carol}'{s} \\ $$$${age}\:{will}\:{be}\:{twice}\:{the}\:{sum}\:{of}\:{Hondo}'{s} \\ $$$${and}\:{Baby}'{s}\:{age}.{How}\:{old}\:{is}\:{each}\:{perso} \\ $$$${n}\:{now}? \\ $$

Question Number 27567    Answers: 0   Comments: 0

f(x)=3x^2 (a)Find the critical number (b)Find the interval on which f increase and decrese (c)Find the local extrem value of f (d)using the 2^(nd) derivative, find local extrem

$$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3x}^{\mathrm{2}} \\ $$$$\left(\mathrm{a}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{critical}\:\mathrm{number} \\ $$$$\left(\mathrm{b}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{interval}\:\mathrm{on}\:\mathrm{which}\:\mathrm{f} \\ $$$$\mathrm{increase}\:\mathrm{and}\:\mathrm{decrese} \\ $$$$\left(\mathrm{c}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{local}\:\mathrm{extrem}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f} \\ $$$$\left(\mathrm{d}\right)\mathrm{using}\:\mathrm{the}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{derivative}, \\ $$$$\mathrm{find}\:\mathrm{local}\:\mathrm{extrem} \\ $$

Question Number 27564    Answers: 0   Comments: 4

Question Number 27563    Answers: 0   Comments: 0

The absolute value of ∫_(10) ^(19) ((cos x)/(1+x^8 )) dx is

$$\mathrm{The}\:\mathrm{absolute}\:\mathrm{value}\:\mathrm{of}\:\underset{\mathrm{10}} {\overset{\mathrm{19}} {\int}}\:\frac{\mathrm{cos}\:{x}}{\mathrm{1}+{x}^{\mathrm{8}} }\:{dx}\:\:\mathrm{is} \\ $$

Question Number 27561    Answers: 0   Comments: 1

a penduum bob is operated by a thread of breadth 100cn and the bob is pulled aside untill the string makes an angle of 60°. calculate (i)the velocity of the bob when the string is vertiv

$${a}\:{penduum}\:{bob}\:{is}\:{operated}\:{by}\:{a}\: \\ $$$${thread}\:{of}\:{breadth}\:\mathrm{100}{cn}\:{and}\:{the} \\ $$$${bob}\:{is}\:{pulled}\:{aside}\:{untill}\:{the}\:{string} \\ $$$${makes}\:{an}\:{angle}\:{of}\:\mathrm{60}°.\:{calculate} \\ $$$$\left({i}\right){the}\:{velocity}\:{of}\:{the}\:{bob}\:{when} \\ $$$${the}\:{string}\:{is}\:{vertiv} \\ $$

Question Number 27559    Answers: 2   Comments: 1

Change in Q#27507 Solve simultaneously: 2(√x)+y=13 x+2(√y)=10

$$\mathrm{Change}\:\mathrm{in}\:\mathrm{Q}#\mathrm{27507} \\ $$$$\mathrm{Solve}\:\mathrm{simultaneously}: \\ $$$$\mathrm{2}\sqrt{\mathrm{x}}+\mathrm{y}=\mathrm{13} \\ $$$$\mathrm{x}+\mathrm{2}\sqrt{\mathrm{y}}=\mathrm{10} \\ $$

Question Number 27547    Answers: 0   Comments: 0

let give A=(_(1 −1) ^(1 1) ) find A^n and e^A .

$${let}\:{give}\:{A}=\left(_{\mathrm{1}\:\:\:\:\:\:\:\:\:−\mathrm{1}} ^{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\mathrm{1}} \right)\:\:\:\:\:{find}\:{A}^{{n}} \:\:\:{and}\:\:{e}^{{A}} \:\:\:. \\ $$

Question Number 27538    Answers: 0   Comments: 0

Question Number 27536    Answers: 0   Comments: 0

m_1 s_1 (x−𝛉)=m_2 s_2 (𝛉−y) ; x=? ;y=? 𝛉=? solve it as an equation....

$$\boldsymbol{\mathrm{m}}_{\mathrm{1}} \boldsymbol{\mathrm{s}}_{\mathrm{1}} \left(\boldsymbol{\mathrm{x}}−\boldsymbol{\theta}\right)=\boldsymbol{\mathrm{m}}_{\mathrm{2}} \boldsymbol{\mathrm{s}}_{\mathrm{2}} \left(\boldsymbol{\theta}−\boldsymbol{\mathrm{y}}\right)\:\:\:;\:\boldsymbol{\mathrm{x}}=?\:;\boldsymbol{\mathrm{y}}=?\:\boldsymbol{\theta}=? \\ $$$$\mathrm{solve}\:\mathrm{it}\:\mathrm{as}\:\mathrm{an}\:\mathrm{equation}.... \\ $$

Question Number 27531    Answers: 0   Comments: 5

(√(1−cos θ/1+cos θ))=?

$$\sqrt{\mathrm{1}−\mathrm{cos}\:\theta/\mathrm{1}+\mathrm{cos}\:\theta}=? \\ $$

  Pg 1814      Pg 1815      Pg 1816      Pg 1817      Pg 1818      Pg 1819      Pg 1820      Pg 1821      Pg 1822      Pg 1823   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com