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Question Number 28694    Answers: 0   Comments: 1

find the value of ∫_0 ^∞ e^(−tx^2 ) cosx dx with t>0 .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{tx}^{\mathrm{2}} } {cosx}\:{dx}\:\:{with}\:{t}>\mathrm{0}\:. \\ $$

Question Number 28690    Answers: 0   Comments: 5

Question Number 28687    Answers: 0   Comments: 0

find the value of ∫_0 ^∞ e^(−( t^2 +(1/t^2 ))) dt.

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left(\:{t}^{\mathrm{2}} +\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right)} {dt}. \\ $$

Question Number 28685    Answers: 0   Comments: 0

find the value of I=∫∫_D x^3 dxdy with D= {(x,y)∈R^2 /1≤x≤2 and x^2 −y^2 ≥1 }.

$${find}\:{the}\:{value}\:{of}\:\:{I}=\int\int_{{D}} \:{x}^{\mathrm{3}} {dxdy}\:\:\:{with} \\ $$$${D}=\:\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\mathrm{1}\leqslant{x}\leqslant\mathrm{2}\:{and}\:\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \:\:\geqslant\mathrm{1}\:\:\right\}. \\ $$

Question Number 28684    Answers: 0   Comments: 0

find sum of S(x)= Σ_(n=1) ^∞ (−1)^(n−1) (x^(2n+1) /(4n^2 −1)) .

$${find}\:\:{sum}\:{of}\:{S}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \:\:\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:. \\ $$

Question Number 28683    Answers: 0   Comments: 1

developp f(x)=e^(−αx) 2π periodic at Fourier serie with α>0.

$${developp}\:{f}\left({x}\right)={e}^{−\alpha{x}} \:\:\:\mathrm{2}\pi\:{periodic}\:{at}\:{Fourier}\:{serie}\:{with} \\ $$$$\alpha>\mathrm{0}. \\ $$

Question Number 28682    Answers: 0   Comments: 2

nature of the serie Σ_(n=0) ^∞ tan(((2n+1)/n^3 )) .

$${nature}\:{of}\:{the}\:{serie}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{tan}\left(\frac{\mathrm{2}{n}+\mathrm{1}}{{n}^{\mathrm{3}} }\right)\:. \\ $$

Question Number 28681    Answers: 0   Comments: 0

give a equivalent of w_n = Σ_(k=n+1) ^∞ (1/(k!)) .

$${give}\:{a}\:{equivalent}\:{of}\:\:{w}_{{n}} =\:\:\:\sum_{{k}={n}+\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{k}!}\:\:. \\ $$

Question Number 28680    Answers: 0   Comments: 0

find lim_(ξ→0) ∫_0 ^(π/2) (dx/(√(sin^2 x +ξcos^2 x))) .

$${find}\:\:{lim}_{\xi\rightarrow\mathrm{0}} \:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{dx}}{\sqrt{{sin}^{\mathrm{2}} {x}\:+\xi{cos}^{\mathrm{2}} {x}}}\:\:\:\:\:. \\ $$

Question Number 28679    Answers: 0   Comments: 1

f function contnue on [0,1] .prove that lim_(n→+∞) n∫_0 ^1 t^n f(t)dt=f(1).

$${f}\:{function}\:{contnue}\:{on}\:\left[\mathrm{0},\mathrm{1}\right]\:.{prove}\:{that} \\ $$$${lim}_{{n}\rightarrow+\infty} \:\:{n}\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{t}^{{n}} {f}\left({t}\right){dt}={f}\left(\mathrm{1}\right). \\ $$

Question Number 28678    Answers: 0   Comments: 0

let give A= (((1 (α/n))),((−(α/n) 1)) ) with n ∈N^∗ and α∈R find lim_(n→+∞) A^n .

$${let}\:{give}\:{A}=\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\frac{\alpha}{{n}}}\\{−\frac{\alpha}{{n}}\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$${with}\:{n}\:\in{N}^{\ast} \:\:{and}\:\alpha\in{R}\:\:\:{find}\:\:{lim}_{{n}\rightarrow+\infty} {A}^{{n}} \:\:. \\ $$

Question Number 28677    Answers: 0   Comments: 1

find ∫_0 ^1 ((lnx)/(x−1))dx

$${find}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{lnx}}{{x}−\mathrm{1}}{dx} \\ $$

Question Number 28676    Answers: 0   Comments: 1

let give u_n = ∫_(nπ) ^((n+1)π) e^(−λt) ((sint)/(√t)) with λ>0 calculate Σ_(n=0) ^(+∞) u_n .

$${let}\:{give}\:\:{u}_{{n}} =\:\int_{{n}\pi} ^{\left({n}+\mathrm{1}\right)\pi} \:\:{e}^{−\lambda{t}} \:\frac{{sint}}{\sqrt{{t}}}\:\:\:\:{with}\:\lambda>\mathrm{0} \\ $$$${calculate}\:\sum_{{n}=\mathrm{0}} ^{+\infty} \:\:\:{u}_{{n}} \:.\: \\ $$$$ \\ $$

Question Number 28756    Answers: 0   Comments: 1

find in terms of λ ∫_0 ^∞ e^(−λt) ((sint)/(√t)) dt with λ>0

$${find}\:{in}\:{terms}\:{of}\:\lambda\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\lambda{t}} \:\frac{{sint}}{\sqrt{{t}}}\:{dt}\:\:{with}\:\:\lambda>\mathrm{0} \\ $$

Question Number 28648    Answers: 0   Comments: 0

If θ = log_e [tanh(((3π)/8))] , Prove that 3tanh(2θ) = 2(√2)

$$\mathrm{If}\:\:\theta\:\:=\:\:\mathrm{log}_{\mathrm{e}} \left[\mathrm{tanh}\left(\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\right]\:,\:\:\:\mathrm{Prove}\:\mathrm{that}\:\:\:\:\:\:\:\mathrm{3tanh}\left(\mathrm{2}\theta\right)\:=\:\mathrm{2}\sqrt{\mathrm{2}} \\ $$

Question Number 28646    Answers: 1   Comments: 0

An object of mass 24kg is accelerated up a frictionless plane inclined at an angle of 37°. Starting at the bottom from the rest,it covers a distance of 18m in 3secs. a)what is the average power required to accomplish the process? b)what is the instantaneous power required at the end of the 3second interval?

$${An}\:{object}\:{of}\:{mass}\:\mathrm{24}{kg}\:{is} \\ $$$${accelerated}\:{up}\:{a}\:{frictionless}\:{plane} \\ $$$${inclined}\:{at}\:{an}\:{angle}\:{of}\:\mathrm{37}°. \\ $$$${Starting}\:{at}\:{the}\:{bottom}\:{from}\:{the} \\ $$$${rest},{it}\:{covers}\:{a}\:{distance}\:{of}\:\mathrm{18}{m} \\ $$$${in}\:\mathrm{3}{secs}. \\ $$$$\left.{a}\right){what}\:{is}\:{the}\:{average}\:{power} \\ $$$${required}\:{to}\:{accomplish}\:{the} \\ $$$${process}? \\ $$$$\left.{b}\right){what}\:{is}\:{the}\:{instantaneous}\:{power} \\ $$$${required}\:{at}\:{the}\:{end}\:{of}\:{the}\:\mathrm{3}{second} \\ $$$${interval}? \\ $$

Question Number 28644    Answers: 0   Comments: 4

A man pushes a box of 40kg up an incline plane of 15°,if the man applies a horizontal force of 200N and the box moves up the plane a distance of 20m at a constant velocity and the coefficient of friction is 0.10, find a)workdone by the man on the box. b)workdone against friction.

$${A}\:{man}\:{pushes}\:{a}\:{box}\:{of}\:\mathrm{40}{kg}\:{up} \\ $$$${an}\:{incline}\:{plane}\:{of}\:\mathrm{15}°,{if}\:{the}\:{man} \\ $$$${applies}\:{a}\:{horizontal}\:{force}\:{of} \\ $$$$\mathrm{200}{N}\:{and}\:{the}\:{box}\:{moves}\:{up}\:{the} \\ $$$${plane}\:{a}\:{distance}\:{of}\:\mathrm{20}{m}\:{at}\:{a} \\ $$$${constant}\:{velocity}\:{and}\:{the} \\ $$$${coefficient}\:{of}\:{friction}\:{is}\:\mathrm{0}.\mathrm{10}, \\ $$$${find}\: \\ $$$$\left.{a}\right){workdone}\:{by}\:{the}\:{man}\:{on}\:{the} \\ $$$${box}. \\ $$$$\left.{b}\right){workdone}\:{against}\:{friction}. \\ $$

Question Number 28643    Answers: 0   Comments: 0

Question Number 28642    Answers: 0   Comments: 0

f(x)=4x−1for0<x<4 find f(0) ,f(1) f(1.2),f(4),f(−1)

$${f}\left({x}\right)=\mathrm{4}{x}−\mathrm{1}{for}\mathrm{0}<{x}<\mathrm{4}\:{find}\:{f}\left(\mathrm{0}\right)\:,{f}\left(\mathrm{1}\right) \\ $$$${f}\left(\mathrm{1}.\mathrm{2}\right),{f}\left(\mathrm{4}\right),{f}\left(−\mathrm{1}\right) \\ $$

Question Number 28640    Answers: 2   Comments: 2

Each of the angle between vectors a, b and c is equal to 60°. If ∣a∣=4, ∣b∣=2 and ∣c∣=6, then the modulus of a+b+c is

$$\mathrm{Each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{between}\:\mathrm{vectors}\:\boldsymbol{\mathrm{a}}, \\ $$$$\boldsymbol{\mathrm{b}}\:\mathrm{and}\:\boldsymbol{\mathrm{c}}\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{60}°.\:\mathrm{If}\:\mid\boldsymbol{\mathrm{a}}\mid=\mathrm{4},\:\mid\boldsymbol{\mathrm{b}}\mid=\mathrm{2} \\ $$$$\mathrm{and}\:\mid\boldsymbol{\mathrm{c}}\mid=\mathrm{6},\:\mathrm{then}\:\mathrm{the}\:\mathrm{modulus}\:\mathrm{of} \\ $$$$\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}\:\:\mathrm{is} \\ $$

Question Number 28626    Answers: 0   Comments: 9

Question Number 28624    Answers: 1   Comments: 4

Question Number 28622    Answers: 0   Comments: 2

find Σ_(k=0) ^(+∞) arctan( (1/(k^2 +k+1))) .

$${find}\:\:\sum_{{k}=\mathrm{0}} ^{+\infty} \:{arctan}\left(\:\frac{\mathrm{1}}{{k}^{\mathrm{2}} +{k}+\mathrm{1}}\right)\:. \\ $$

Question Number 28621    Answers: 0   Comments: 0

let give u_n =(([(√(n+1])) −[(√(n])))/n) find Σ u_n .

$${let}\:{give}\:{u}_{{n}} =\frac{\left[\sqrt{\left.{n}+\mathrm{1}\right]}\:−\left[\sqrt{\left.{n}\right]}\right.\right.}{{n}}\:\:\:{find}\:\:\Sigma\:{u}_{{n}} \:\:. \\ $$

Question Number 28620    Answers: 0   Comments: 4

calculate Σ_(n=p) ^(+∞) C_(n ) ^p x^n .

$${calculate}\:\:\sum_{{n}={p}} ^{+\infty} \:\:\:{C}_{{n}\:} ^{{p}} {x}^{{n}} . \\ $$

Question Number 28619    Answers: 0   Comments: 1

calculate Σ_(k=2) ^(+∞) ln(1−(1/k^2 )) .

$${calculate}\:\:\sum_{{k}=\mathrm{2}} ^{+\infty} \:{ln}\left(\mathrm{1}−\frac{\mathrm{1}}{{k}^{\mathrm{2}} }\right)\:. \\ $$

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