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Question Number 28434 Answers: 0 Comments: 0

let give the polynomial p(x)=(x+1)^n −(x−1)^n with n from N^∗ 1) give the factorisation of p(x) inside C[x] 2) prove that Π_(k=0) ^(n−1) cotan(((kπ)/(2p+1)))=(1/(√(2p+1)))

$${let}\:{give}\:{the}\:{polynomial}\:{p}\left({x}\right)=\left({x}+\mathrm{1}\right)^{{n}} −\left({x}−\mathrm{1}\right)^{{n}} {with}\:{n} \\ $$$${from}\:{N}^{\ast} \\ $$$$\left.\mathrm{1}\right)\:{give}\:{the}\:{factorisation}\:{of}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} {cotan}\left(\frac{{k}\pi}{\mathrm{2}{p}+\mathrm{1}}\right)=\frac{\mathrm{1}}{\sqrt{\mathrm{2}{p}+\mathrm{1}}} \\ $$

Question Number 28433 Answers: 0 Comments: 0

let give T_n (x)= cos(narcosx) decompose (1/(T_n (x))).

$${let}\:{give}\:{T}_{{n}} \left({x}\right)=\:{cos}\left({narcosx}\right)\:\:{decompose}\:\frac{\mathrm{1}}{{T}_{{n}} \left({x}\right)}. \\ $$

Question Number 28432 Answers: 0 Comments: 1

let put w=e^(i((2π)/n)) calculate S_n = Σ_(k=0) ^(n−1) (1/(x−w^k )) and W_n = Σ_(k=0) ^(n−1) (1/((x−w^k )^2 )) .

$${let}\:{put}\:{w}={e}^{{i}\frac{\mathrm{2}\pi}{{n}}} \:{calculate}\:\:{S}_{{n}} =\:\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:\:\frac{\mathrm{1}}{{x}−{w}^{{k}} }\:\:{and} \\ $$$${W}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:\frac{\mathrm{1}}{\left({x}−{w}^{{k}} \right)^{\mathrm{2}} }\:. \\ $$

Question Number 28431 Answers: 0 Comments: 0

let give w_k = e^(i((2kπ)/n)) k∈Z find the value of Π_(k=0) ^(n−1) (1+(2/(2−w_k ))).

$${let}\:{give}\:{w}_{{k}} =\:{e}^{{i}\frac{\mathrm{2}{k}\pi}{{n}}} \:\:\:{k}\in{Z}\:\:\:{find}\:{the}\:{value}\:{of} \\ $$$$\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left(\mathrm{1}+\frac{\mathrm{2}}{\mathrm{2}−{w}_{{k}} \:}\right). \\ $$

Question Number 28430 Answers: 0 Comments: 1

let give A_n = ∫_0 ^n (1+(x/n))^n e^(−2x) dx lim_(n→∝) A_n ?

$${let}\:{give}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\left(\mathrm{1}+\frac{{x}}{{n}}\right)^{{n}} {e}^{−\mathrm{2}{x}} {dx}\:\:\:{lim}_{{n}\rightarrow\propto} \:{A}_{{n}} ? \\ $$$$ \\ $$

Question Number 28429 Answers: 0 Comments: 1

find lim_(x→0) ∫_(x+1) ^(2x+1) (t^2 /(ln(1+t)))dt .

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\int_{{x}+\mathrm{1}} ^{\mathrm{2}{x}+\mathrm{1}} \:\:\frac{{t}^{\mathrm{2}} }{{ln}\left(\mathrm{1}+{t}\right)}{dt}\:\:. \\ $$

Question Number 28428 Answers: 0 Comments: 1

let give f_n (x)= ((x^2 −1)^n )^((n)) find f_n .

$${let}\:{give}\:{f}_{{n}} \left({x}\right)=\:\left(\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{{n}} \right)^{\left({n}\right)} \:\:\:{find}\:\:{f}_{{n}} \:. \\ $$

Question Number 28427 Answers: 1 Comments: 1

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

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

Question Number 28426 Answers: 0 Comments: 0

find lim_(x→0) (((1+sinx)^(1/x) −e^(1−(x/2)) )/((1+tanx)^(1/x) − e^(1−(x/2)) )) .

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{\left(\mathrm{1}+{sinx}\right)^{\frac{\mathrm{1}}{{x}}} \:\:−{e}^{\mathrm{1}−\frac{{x}}{\mathrm{2}}} }{\left(\mathrm{1}+{tanx}\right)^{\frac{\mathrm{1}}{{x}}} −\:\:{e}^{\mathrm{1}−\frac{{x}}{\mathrm{2}}} }\:. \\ $$

Question Number 28417 Answers: 0 Comments: 0

Question Number 28413 Answers: 0 Comments: 0

Question Number 28408 Answers: 0 Comments: 0

Determine (i) (∞/a) (ii) ((−∞)/a) in case (a) a∈R^− (b) a∈R^+

$$\mathrm{Determine}\:\left(\mathrm{i}\right)\:\frac{\infty}{{a}}\:\:\left(\mathrm{ii}\right)\:\frac{−\infty}{{a}}\:\mathrm{in}\:\mathrm{case}\: \\ $$$$\left({a}\right)\:{a}\in\mathbb{R}^{−} \:\:\:\:\left({b}\right)\:\:{a}\in\mathbb{R}^{+} \\ $$

Question Number 28406 Answers: 1 Comments: 1

Image not getting attached. Please see the link below.

$${Image}\:{not}\:{getting}\:{attached}.\:{Please} \\ $$$${see}\:{the}\:{link}\:{below}. \\ $$

Question Number 28399 Answers: 1 Comments: 0

Question Number 28411 Answers: 2 Comments: 1

Question Number 28393 Answers: 0 Comments: 0

Find the value of Σ_(i = 0) ^(33) (((99)),((3k)) )

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\underset{{i}\:=\:\mathrm{0}} {\overset{\mathrm{33}} {\sum}}\:\begin{pmatrix}{\mathrm{99}}\\{\mathrm{3}{k}}\end{pmatrix} \\ $$

Question Number 28384 Answers: 2 Comments: 0

Question Number 28382 Answers: 1 Comments: 0

A boat of mass m, traveling with v of Vo at t=0. A power is shut off assuming water resistance is proportioal to Vn^ and V is instantaneous velocity find V as a function of the distance travelled

$${A}\:{boat}\:{of}\:{mass}\:{m},\:{traveling}\:{with}\:{v}\:{of}\:{Vo}\:{at} \\ $$$${t}=\mathrm{0}.\:{A}\:{power}\:{is}\:{shut}\:{off}\:{assuming}\:{water}\: \\ $$$${resistance}\:{is}\:{proportioal}\:{to}\:{V}\hat {{n}}\:\:{and}\:{V}\:{is}\: \\ $$$${instantaneous}\:{velocity}\:{find}\:{V}\:{as}\:{a}\:{function} \\ $$$${of}\:{the}\:{distance}\:{travelled} \\ $$

Question Number 28381 Answers: 0 Comments: 0

Question Number 28375 Answers: 1 Comments: 0

4kg ball falls from rest at time t =0 in a medium offering a resistance in kg numerically equal to twice its instantaneous velocity in m/s. find; (a) the velocity and distance travelled at any time t>0 (b) the limiting velocity

$$\:\mathrm{4}{kg}\:{ball}\:{falls}\:{from}\:{rest}\:{at}\:{time}\:{t}\:=\mathrm{0}\:{in}\:{a}\: \\ $$$${medium}\:{offering}\:\:{a}\:{resistance}\:{in}\:{kg}\: \\ $$$${numerically}\:{equal}\:{to}\:{twice}\:{its}\:{instantaneous} \\ $$$${velocity}\:{in}\:{m}/{s}. \\ $$$${find}; \\ $$$$\left({a}\right)\:{the}\:{velocity}\:{and}\:{distance}\:{travelled}\:{at}\:{any}\: \\ $$$${time}\:{t}>\mathrm{0}\: \\ $$$$\left({b}\right)\:{the}\:{limiting}\:{velocity}\: \\ $$

Question Number 28373 Answers: 1 Comments: 0

What is the implication of connecting a low resistance in series to a galvanometer?

$${What}\:{is}\:{the}\:{implication}\:{of} \\ $$$${connecting}\:{a}\:{low}\:{resistance}\:{in}\: \\ $$$${series}\:{to}\:{a}\:{galvanometer}? \\ $$

Question Number 28372 Answers: 0 Comments: 0

let give w=e^(i2(π/n)) .calculate Π_(l=0_(l≠k) ) ^(n−1) (w^k −w^l ) .

$${let}\:{give}\:{w}={e}^{{i}\mathrm{2}\frac{\pi}{{n}}} \:\:\:\:.{calculate}\:\:\prod_{{l}=\mathrm{0}_{{l}\neq{k}} } ^{{n}−\mathrm{1}} \:\:\:\left({w}^{{k}} \:\:−{w}^{{l}} \right)\:. \\ $$

Question Number 28371 Answers: 0 Comments: 1

prove that x^2 −2x cosθ +1 divide x^(2n) −2x^n cos(nθ)+1

$${prove}\:{that}\:{x}^{\mathrm{2}} −\mathrm{2}{x}\:{cos}\theta\:+\mathrm{1}\:{divide}\:{x}^{\mathrm{2}{n}} \:−\mathrm{2}{x}^{{n}} {cos}\left({n}\theta\right)+\mathrm{1} \\ $$

Question Number 28370 Answers: 0 Comments: 1

1) factorizse p(x) =x^n −1 inside C[x] 2) find the value of Π_(k=1) ^(n−1) sin(((kπ)/n)) 3)find also the value of Π_(k=0) ^(n−1) sin(((kπ)/n) +θ).

$$\left.\mathrm{1}\right)\:{factorizse}\:{p}\left({x}\right)\:={x}^{{n}} \:−\mathrm{1}\:\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\prod_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \:{sin}\left(\frac{{k}\pi}{{n}}\right) \\ $$$$\left.\mathrm{3}\right){find}\:{also}\:{the}\:{value}\:{of}\:\:\:\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:{sin}\left(\frac{{k}\pi}{{n}}\:+\theta\right). \\ $$

Question Number 28369 Answers: 0 Comments: 0

let give the matrice A = (((1 0 0)),((0 1 1)) ) [ (1 0 1 A ∈ M_3 (R) write A at form A= I +J and calculate A^n .

$${let}\:{give}\:{the}\:{matrice}\:\:\:{A}\:=\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{1}\right.\right. \\ $$$${A}\:\in\:{M}_{\mathrm{3}} \left({R}\right)\:\:{write}\:\:{A}\:{at}\:{form}\:\:{A}=\:{I}\:+{J}\:\:\:\:{and}\:{calculate} \\ $$$${A}^{{n}} . \\ $$

Question Number 28368 Answers: 0 Comments: 0

P is apolynomial from C_n [x] having n roots (x_i )_(1≤i≤n ) and x_i # x_j for i#j 1) prove that Σ_(i=1) ^n (1/(p^′ (x_i ))) =0 2) find Σ_(i=1) ^n (x_i ^k /(p^′ (x_i ))) with k∈[[0,n−1]] .

$${P}\:{is}\:{apolynomial}\:{from}\:{C}_{{n}} \left[{x}\right]\:{having}\:{n}\:{roots} \\ $$$$\left({x}_{{i}} \right)_{\mathrm{1}\leqslant{i}\leqslant{n}\:} \:\:\:\:{and}\:{x}_{{i}} #\:{x}_{{j}} \:{for}\:{i}#{j} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\:\sum_{{i}=\mathrm{1}} ^{{n}} \:\:\:\frac{\mathrm{1}}{{p}^{'} \left({x}_{{i}} \right)}\:\:=\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:\:\:\:\sum_{{i}=\mathrm{1}} ^{{n}} \:\:\:\frac{{x}_{{i}} ^{{k}} }{{p}^{'} \left({x}_{{i}} \right)}\:\:\:\:{with}\:{k}\in\left[\left[\mathrm{0},{n}−\mathrm{1}\right]\right]\:\:. \\ $$

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