Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1687

Question Number 31502    Answers: 0   Comments: 3

find f(x)= ∫_0 ^1 ln(1+xt^2 )dt with x>0. 2) give thevalue of ∫_0 ^1 ln(1+t^2 )dt and ∫_0 ^1 ln(1+2t^2 )dt.

$${find}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right){dt}\:\:{with}\:{x}>\mathrm{0}. \\ $$$$\left.\mathrm{2}\right)\:{give}\:{thevalue}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right){dt}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} \right){dt}. \\ $$

Question Number 31501    Answers: 0   Comments: 1

find ∫_0 ^(π/4) ln(1 +2tanx)dx.

$${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}\:+\mathrm{2}{tanx}\right){dx}. \\ $$

Question Number 31500    Answers: 0   Comments: 3

let L_n (x)= e^x (e^(−x) x^n )^((n)) 1) prove that L_n is a polynomial 2) find degL_(n ) and the leading coefficient .

$${let}\:{L}_{{n}} \left({x}\right)=\:{e}^{{x}} \:\left({e}^{−{x}} \:{x}^{{n}} \right)^{\left({n}\right)} \: \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{L}_{{n}} \:{is}\:{a}\:{polynomial} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{degL}_{{n}\:} {and}\:{the}\:{leading}\:{coefficient}\:. \\ $$

Question Number 31499    Answers: 0   Comments: 1

find the polynial p wich verify p(x)−p^′ (x)=x^n then calculate ∫_0 ^1 p(x)dx.

$${find}\:{the}\:{polynial}\:{p}\:{wich}\:{verify}\:{p}\left({x}\right)−{p}^{'} \left({x}\right)={x}^{{n}} \:{then} \\ $$$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {p}\left({x}\right){dx}. \\ $$

Question Number 31498    Answers: 0   Comments: 0

find tbe value of Π_(k=1) ^n sin(((kπ)/(n+1))).

$${find}\:{tbe}\:{value}\:{of}\:\prod_{{k}=\mathrm{1}} ^{{n}} \:{sin}\left(\frac{{k}\pi}{{n}+\mathrm{1}}\right). \\ $$

Question Number 31496    Answers: 0   Comments: 1

let a∈]0,π[ and A(x)= x^(2n) −2cos(na)x^n +1 1)factorize inside C[x] A(x) 2) factorize inside R[x] A(x).

$$\left.{let}\:{a}\in\right]\mathrm{0},\pi\left[\:\:\:{and}\:{A}\left({x}\right)=\:{x}^{\mathrm{2}{n}} \:−\mathrm{2}{cos}\left({na}\right){x}^{{n}} \:+\mathrm{1}\right. \\ $$$$\left.\mathrm{1}\right){factorize}\:{inside}\:{C}\left[{x}\right]\:{A}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{inside}\:{R}\left[{x}\right]\:{A}\left({x}\right). \\ $$

Question Number 31495    Answers: 0   Comments: 0

let give p(x)=(x+j)^n −(x−j)^n with j=e^(i((2π)/3)) 1) find roots of p(x) 2) factorize inside C[ x] p(x) 3)factorize inside R[x] p(x).

$${let}\:{give}\:{p}\left({x}\right)=\left({x}+{j}\right)^{{n}} \:−\left({x}−{j}\right)^{{n}} \:{with}\:{j}={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{inside}\:{C}\left[\:{x}\right]\:{p}\left({x}\right) \\ $$$$\left.\mathrm{3}\right){factorize}\:{inside}\:{R}\left[{x}\right]\:{p}\left({x}\right). \\ $$

Question Number 31494    Answers: 0   Comments: 3

prove that x^2 divide (x+1)^n_ −nx−1 .nintegr.

$${prove}\:{that}\:{x}^{\mathrm{2}} \:{divide}\:\left({x}+\mathrm{1}\right)^{\underset{} {{n}}} \:−{nx}−\mathrm{1}\:.{nintegr}. \\ $$

Question Number 31493    Answers: 0   Comments: 0

if (xcosθ +sint)^n =Q(x^2 +1) +R find tbe polynomialR

$${if}\:\left({xcos}\theta\:+{sint}\right)^{{n}} \:={Q}\left({x}^{\mathrm{2}} +\mathrm{1}\right)\:+{R}\:\:{find}\:{tbe}\:{polynomialR} \\ $$

Question Number 31492    Answers: 0   Comments: 0

find all polynomial p(x) wich verify ∀k∈Z ∫_k ^(k+1) p(x)dx=k+1.

$${find}\:{all}\:{polynomial}\:{p}\left({x}\right)\:{wich}\:{verify}\: \\ $$$$\forall{k}\in{Z}\:\:\:\int_{{k}} ^{{k}+\mathrm{1}} {p}\left({x}\right){dx}={k}+\mathrm{1}. \\ $$

Question Number 31491    Answers: 0   Comments: 0

let p(x)= x^n +a_(n−1) x^(n−1) +.... a_1 x +a_o if ξ is roots of p(x) prove that ∣ξ∣ ≤ 1+max_(0≤i≤n−1) ∣a_i ∣

$${let}\:{p}\left({x}\right)=\:{x}^{{n}} \:+{a}_{{n}−\mathrm{1}} {x}^{{n}−\mathrm{1}} \:+....\:{a}_{\mathrm{1}} {x}\:+{a}_{{o}} \\ $$$${if}\:\:\xi\:\:{is}\:{roots}\:{of}\:{p}\left({x}\right)\:{prove}\:{that}\:\mid\xi\mid\:\leqslant\:\mathrm{1}+{max}_{\mathrm{0}\leqslant{i}\leqslant{n}−\mathrm{1}} \:\mid{a}_{{i}} \mid \\ $$

Question Number 31490    Answers: 0   Comments: 0

simplify p(x)= (1+x^2 )(1+x^4 )....(1+x^(2n) ) with n fromN then find the roots of p(x).

$${simplify}\:{p}\left({x}\right)=\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}} \right)....\left(\mathrm{1}+{x}^{\mathrm{2}{n}} \right)\:{with}\:{n}\:{fromN} \\ $$$${then}\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right). \\ $$

Question Number 31485    Answers: 2   Comments: 0

Question Number 31524    Answers: 0   Comments: 1

find lim_(n→∞) (1+sin((1/n)))^n .

$${find}\:{lim}_{{n}\rightarrow\infty} \left(\mathrm{1}+{sin}\left(\frac{\mathrm{1}}{{n}}\right)\right)^{{n}} . \\ $$

Question Number 31476    Answers: 1   Comments: 0

From a circular disc of radius R a circular hole of radius R/2 is cut out.The centre of the circular hole is at R/2 from the centre of the original disc.Locate the centre of gravity of the resulting flat body. please help me as fast as possible. Thanks!

$${From}\:{a}\:{circular}\:{disc}\:{of}\:{radius}\:{R} \\ $$$${a}\:{circular}\:{hole}\:{of}\:{radius}\:{R}/\mathrm{2}\:{is} \\ $$$${cut}\:{out}.{The}\:{centre}\:{of}\:{the}\:{circular} \\ $$$${hole}\:{is}\:{at}\:{R}/\mathrm{2}\:{from}\:{the}\:{centre}\:{of} \\ $$$${the}\:{original}\:{disc}.{Locate}\:{the}\:{centre} \\ $$$${of}\:{gravity}\:{of}\:{the}\:{resulting}\:{flat} \\ $$$${body}. \\ $$$$ \\ $$$${please}\:{help}\:{me}\:{as}\:{fast}\:{as}\:{possible}. \\ $$$${Thanks}! \\ $$

Question Number 31475    Answers: 0   Comments: 0

Question Number 31474    Answers: 1   Comments: 1

A vacuum chamber has a door with surface dimensions 20cm×20cm.How many 70kg men, each exerting a pull equal to his weight,will it take to pull the door open when the chamber is evacuated to a pressure of 0.1 atm?

$${A}\:{vacuum}\:{chamber}\:{has}\:{a}\:{door} \\ $$$${with}\:{surface}\:{dimensions} \\ $$$$\mathrm{20}{cm}×\mathrm{20}{cm}.{How}\:{many}\:\mathrm{70}{kg}\:{men}, \\ $$$${each}\:{exerting}\:{a}\:{pull}\:{equal}\:{to}\:{his} \\ $$$${weight},{will}\:{it}\:{take}\:{to}\:{pull}\:{the} \\ $$$${door}\:{open}\:{when}\:{the}\:{chamber}\:{is} \\ $$$${evacuated}\:{to}\:{a}\:{pressure}\:{of}\:\mathrm{0}.\mathrm{1}\:{atm}? \\ $$

Question Number 31466    Answers: 0   Comments: 0

let give I_n = ∫_(1/n) ^1 (√(1+t^2 )) dt 1) calculate I_n 2) find lim_(n→∞) I_n .

$${let}\:{give}\:{I}_{{n}} =\:\int_{\frac{\mathrm{1}}{{n}}} ^{\mathrm{1}} \:\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:{I}_{{n}} \:\:\:. \\ $$

Question Number 31465    Answers: 0   Comments: 0

find F(α)= ∫_0 ^1 ((arctan(αx))/(1+x^2 )) dx with α ∈ R−{1,−1}

$${find}\:\:{F}\left(\alpha\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:{with}\:\alpha\:\in\:{R}−\left\{\mathrm{1},−\mathrm{1}\right\} \\ $$

Question Number 31464    Answers: 0   Comments: 0

1) find A_n = ∫_0 ^(π/2) e^(−x) cos(nx)dx 2) find S_n = Σ_(k=0) ^n A_k .

$$\left.\mathrm{1}\right)\:{find}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:{e}^{−{x}} {cos}\left({nx}\right){dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{S}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{A}_{{k}} \:\:. \\ $$

Question Number 31463    Answers: 0   Comments: 0

let give the function f(x)=∫_0 ^π ln(1+xcosθ)dθ with ∣x∣<1 1) find a simple form of f(x) 2)calculate ∫_0 ^π ln(1−cosθ)dθ 3)calculate ∫_0 ^π ln(1+cosθ)dθ.

$${let}\:{give}\:{the}\:{function}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} {ln}\left(\mathrm{1}+{xcos}\theta\right){d}\theta\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\mathrm{1}−{cos}\theta\right){d}\theta \\ $$$$\left.\mathrm{3}\right){calculate}\:\int_{\mathrm{0}} ^{\pi} {ln}\left(\mathrm{1}+{cos}\theta\right){d}\theta. \\ $$

Question Number 31462    Answers: 0   Comments: 0

find ∫_0 ^∞ ((arctan(x+(1/x)))/(1+x^2 ))dx.

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left({x}+\frac{\mathrm{1}}{{x}}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}. \\ $$

Question Number 31461    Answers: 0   Comments: 0

let give u_n = Σ_(k=1) ^n sin ((k/n)) sin((k/n^2 )) 1) prove that the sequence (u_n ) is convergent 2) find lim_(n→∞) u_n .

$${let}\:{give}\:\:{u}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{sin}\:\left(\frac{{k}}{{n}}\right)\:{sin}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right) \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{the}\:{sequence}\:\left({u}_{{n}} \right)\:{is}\:{convergent} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:{u}_{{n}} . \\ $$

Question Number 31460    Answers: 0   Comments: 1

find in terms of n the value of A_n = ∫_0 ^1 Π_(k=1) ^(n−1) (x^2 −2xcos(((kπ)/n)) +1)dx with n from N^★ .

$${find}\:{in}\:{terms}\:{of}\:\:{n}\:{the}\:{value}\:{of} \\ $$$${A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\prod_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \left({x}^{\mathrm{2}} \:−\mathrm{2}{xcos}\left(\frac{{k}\pi}{{n}}\right)\:+\mathrm{1}\right){dx}\:\:\:{with}\:{n}\:{from}\:{N}^{\bigstar} . \\ $$

Question Number 31456    Answers: 0   Comments: 2

Find sum of S= (2/3) + (4/3^2 ) + (6/3^3 ) + (8/3^4 ) +......+∞ ?

$$\mathbb{F}{ind}\:{sum}\:{of} \\ $$$${S}=\:\frac{\mathrm{2}}{\mathrm{3}}\:+\:\frac{\mathrm{4}}{\mathrm{3}^{\mathrm{2}} }\:+\:\frac{\mathrm{6}}{\mathrm{3}^{\mathrm{3}} }\:+\:\frac{\mathrm{8}}{\mathrm{3}^{\mathrm{4}} }\:+......+\infty\:? \\ $$

Question Number 31459    Answers: 0   Comments: 0

find ∫_0 ^(π/4) ((cost)/(cos^3 t +sin^3 t)) dt.

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\frac{{cost}}{{cos}^{\mathrm{3}} {t}\:+{sin}^{\mathrm{3}} {t}}\:{dt}. \\ $$

  Pg 1682      Pg 1683      Pg 1684      Pg 1685      Pg 1686      Pg 1687      Pg 1688      Pg 1689      Pg 1690      Pg 1691   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com