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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]] .

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

Question Number 28367 Answers: 0 Comments: 0

find F∈R(x) wich verify F(x+1) −F(x)= ((x+3)/(x(x−1)(x+1))).

$${find}\:{F}\in{R}\left({x}\right)\:\:{wich}\:{verify}\:\:{F}\left({x}+\mathrm{1}\right)\:−{F}\left({x}\right)=\:\frac{{x}+\mathrm{3}}{{x}\left({x}−\mathrm{1}\right)\left({x}+\mathrm{1}\right)}. \\ $$

Question Number 28366 Answers: 0 Comments: 0

let give P(x)= α(x−x_1 )^m_1 (x−x_2 )^m_2 .....(x−x_n )^m_n give the decomposition of F(x)= ((d(P))/P) .d mean derivative

$${let}\:{give}\:{P}\left({x}\right)=\:\alpha\left({x}−{x}_{\mathrm{1}} \right)^{{m}_{\mathrm{1}} } \left({x}−{x}_{\mathrm{2}} \right)^{{m}_{\mathrm{2}} } .....\left({x}−{x}_{{n}} \right)^{{m}_{{n}} } \\ $$$${give}\:{the}\:{decomposition}\:{of}\:{F}\left({x}\right)=\:\frac{{d}\left({P}\right)}{{P}}\:.{d}\:{mean}\:{derivative} \\ $$

Question Number 28364 Answers: 0 Comments: 0

let give F(x) = (1/(x^2 +1)) prove that ∃ P_n ∈ Z_n [x] / F^((n)) (x)= ((P_n (x))/((1+x^2 )^n )) find a relation of recurence between the P_n .prove that all roots of P_n are reals and smples.

$${let}\:{give}\:{F}\left({x}\right)\:=\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\:{prove}\:{that}\:\exists\:{P}_{{n}} \in\:{Z}_{{n}} \left[{x}\right]\:/ \\ $$$${F}^{\left({n}\right)} \left({x}\right)=\:\:\frac{{P}_{{n}} \left({x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:\:\:{find}\:{a}\:{relation}\:{of}\:{recurence}\:{between}\: \\ $$$${the}\:\:{P}_{{n}} \:.{prove}\:{that}\:{all}\:{roots}\:{of}\:{P}_{{n}} \:{are}\:{reals}\:{and}\:{smples}. \\ $$

Question Number 28363 Answers: 1 Comments: 0

simlify the sum S= Σ_(k=0) ^(n−1) ((x+ e^(i2kπ) )/(x −e^(i2kπ) )) .

$${simlify}\:{the}\:{sum}\:\:\:{S}=\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:\frac{{x}+\:{e}^{{i}\mathrm{2}{k}\pi} }{{x}\:−{e}^{{i}\mathrm{2}{k}\pi} }\:\:. \\ $$

Question Number 28359 Answers: 0 Comments: 1

Question Number 28349 Answers: 1 Comments: 1

Question Number 28341 Answers: 1 Comments: 4

Find lim_(x→0) ((5x−tan (5x))/x^3 )

$${Find}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{5}{x}−\mathrm{tan}\:\left(\mathrm{5}{x}\right)}{{x}^{\mathrm{3}} } \\ $$

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