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Question Number 27677 Answers: 1 Comments: 4

Question Number 27681 Answers: 0 Comments: 2

Find square root of 7−30(√2)i .

$${Find}\:{square}\:{root}\:{of}\:\mathrm{7}−\mathrm{30}\sqrt{\mathrm{2}}{i}\:. \\ $$

Question Number 27673 Answers: 0 Comments: 1

Question Number 27667 Answers: 1 Comments: 0

If the ex−radii r_1 , r_2 , r_3 of △ABC are in HP, then its sides are in

$$\mathrm{If}\:\mathrm{the}\:\mathrm{ex}−\mathrm{radii}\:\:{r}_{\mathrm{1}} \:,\:{r}_{\mathrm{2}} \:,\:{r}_{\mathrm{3}} \:\mathrm{of}\:\bigtriangleup{ABC} \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{HP},\:\mathrm{then}\:\mathrm{its}\:\mathrm{sides}\:\mathrm{are}\:\mathrm{in} \\ $$

Question Number 27666 Answers: 0 Comments: 0

let give I_n = ∫_0 ^1 (x^n /(1+x^n ))dx (1) prove that lim_(n−>∝) I_n =0 (2)calculate I_n +I_(n+1) (3) find Σ_(n=1) ^∝ (((−1)^(n−1) )/n) .

$${let}\:{give}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}^{{n}} }{\mathrm{1}+{x}^{{n}} }{dx} \\ $$$$\left(\mathrm{1}\right)\:{prove}\:{that}\:\:{lim}_{{n}−>\propto} {I}_{{n}} =\mathrm{0} \\ $$$$\left(\mathrm{2}\right){calculate}\:{I}_{{n}} \:+{I}_{{n}+\mathrm{1}} \\ $$$$\left(\mathrm{3}\right)\:{find}\:\:\sum_{{n}=\mathrm{1}} ^{\propto} \frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}}\:. \\ $$

Question Number 28200 Answers: 0 Comments: 1

let give I= ∫_0 ^1 ((ln(1+x))/(1+x^2 ))dx and J=∫∫_([0,1]^2 ) (x/((1+x^2 )(1+xy)))dxdy calculate J by two methods then find the value of I.

$${let}\:{give}\:{I}=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:{and}\:{J}=\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\frac{{x}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{xy}\right)}{dxdy} \\ $$$${calculate}\:{J}\:{by}\:{two}\:{methods}\:{then}\:{find}\:{the}\:{value}\:{of}\:{I}. \\ $$

Question Number 27664 Answers: 0 Comments: 1

let give the sequence V_n = Π_(k=1) ^(k=n) (1+(k^2 /n^2 ) )^(1/n) find the value of lim _(n−>∝) V_n .

$${let}\:{give}\:{the}\:{sequence}\:{V}_{{n}} =\:\prod_{{k}=\mathrm{1}} ^{{k}={n}} \left(\mathrm{1}+\frac{{k}^{\mathrm{2}} }{{n}^{\mathrm{2}} }\:\right)^{\frac{\mathrm{1}}{{n}}} \\ $$$${find}\:{the}\:{value}\:{of}\:{lim}\:_{{n}−>\propto} \:{V}_{{n}} \:\:. \\ $$

Question Number 27663 Answers: 0 Comments: 1

let give U_n =n ( (1/n^2 ) + (1/(1^2 +n^2 ))+ (1/(2^2 +n^2 )) +.... (1/((n−1)^2 +n^2 ))) find lim_(n−>∝) U_n .

$${let}\:{give}\:\:{U}_{{n}} ={n}\:\left(\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:\:+\:\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} +{n}^{\mathrm{2}} }+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} +{n}^{\mathrm{2}} }\:+....\:\frac{\mathrm{1}}{\left({n}−\mathrm{1}\right)^{\mathrm{2}} +{n}^{\mathrm{2}} }\right) \\ $$$${find}\:{lim}_{{n}−>\propto} \:\:{U}_{{n}} \:\:\:. \\ $$$$ \\ $$

Question Number 27662 Answers: 0 Comments: 0

factorize in C[x] x^2 +y^2 +z^2 .

$${factorize}\:{in}\:{C}\left[{x}\right]\:\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\:+{z}^{\mathrm{2}} \:\:.\: \\ $$

Question Number 27655 Answers: 0 Comments: 0

what is reration betwen int ensity o diffraction and sli t witdh

$${what}\:{is}\:{reration}\:{betwen}\:{int} \\ $$$${ensity}\:{o}\:{diffraction}\:{and}\:{sli} \\ $$$${t}\:{witdh} \\ $$

Question Number 27643 Answers: 2 Comments: 1

Question Number 27651 Answers: 2 Comments: 2

A positive number has 8 distinct divisors Lets say a, b, c, d, e, f, g and h Given a . b . c . d . e . f . g . h = 3111696 Find that number

$$\mathrm{A}\:\mathrm{positive}\:\mathrm{number}\:\mathrm{has}\:\mathrm{8}\:\mathrm{distinct}\:\mathrm{divisors} \\ $$$$\mathrm{Lets}\:\mathrm{say}\:{a},\:{b},\:{c},\:{d},\:{e},\:{f},\:{g}\:\mathrm{and}\:{h} \\ $$$$\mathrm{Given}\:\:{a}\:.\:{b}\:.\:{c}\:.\:{d}\:.\:{e}\:.\:{f}\:.\:{g}\:.\:{h}\:=\:\mathrm{3111696} \\ $$$$\mathrm{Find}\:\mathrm{that}\:\mathrm{number} \\ $$

Question Number 27640 Answers: 1 Comments: 0

Question Number 27635 Answers: 0 Comments: 0

Question Number 27627 Answers: 1 Comments: 1

Question Number 27624 Answers: 0 Comments: 3

(D^2 +2D+1)y=x^2 +2x+1

$$\left({D}^{\mathrm{2}} +\mathrm{2}{D}+\mathrm{1}\right){y}={x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1} \\ $$

Question Number 27621 Answers: 0 Comments: 0

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

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

Question Number 27620 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ (((−1)^x^2 )/(3+x^2 ))dx .

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{x}^{\mathrm{2}} } }{\mathrm{3}+{x}^{\mathrm{2}} }{dx}\:. \\ $$

Question Number 27619 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ ((cos(2x))/((1+x^2 )^2 ))dx.

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

Question Number 27618 Answers: 1 Comments: 0

Find the range of y=x(x^6 −1).For which y=0

$${Find}\:{the}\:{range}\:{of}\:{y}={x}\left({x}^{\mathrm{6}} −\mathrm{1}\right).{For} \\ $$$${which}\:{y}=\mathrm{0} \\ $$

Question Number 27616 Answers: 0 Comments: 1

find ∫_0 ^1 e^(−2x) ln(1+x)dx .

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−\mathrm{2}{x}} {ln}\left(\mathrm{1}+{x}\right){dx}\:\:. \\ $$

Question Number 27615 Answers: 0 Comments: 2

∫x^(5/2) (1−x)^(3/2) dx

$$\int{x}^{\mathrm{5}/\mathrm{2}} \left(\mathrm{1}−{x}\right)^{\mathrm{3}/\mathrm{2}} {dx} \\ $$

Question Number 27614 Answers: 0 Comments: 2

∫((cosx)/(2−cosx))dx

$$\int\frac{{cosx}}{\mathrm{2}−{cosx}}{dx} \\ $$

Question Number 27613 Answers: 1 Comments: 1

find the value of ∫_0 ^∞ e^(−[x] −x) dx .

$${find}\:{the}\:{value}\:{of}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left[{x}\right]\:−{x}} {dx}\:\:. \\ $$

Question Number 27612 Answers: 1 Comments: 0

∫(1/(3+cos^2 x))dx

$$\int\frac{\mathrm{1}}{\mathrm{3}+{cos}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 27611 Answers: 1 Comments: 0

∫(1/(2sin^2 x + 4cos^2 x))dx

$$\int\frac{\mathrm{1}}{\mathrm{2sin}\:^{\mathrm{2}} {x}\:+\:\mathrm{4cos}\:^{\mathrm{2}} {x}}{dx} \\ $$

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