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Question Number 28165    Answers: 0   Comments: 0

let give w= e^(i((2π)/n)) calculate Σ_(k=0) ^(n−1) (1+w^k )^n .

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

Question Number 28164    Answers: 1   Comments: 0

simplify A=cos^4 θ +cos^4 (θ+(π/4)) +cos^4 (θ +((2π)/4)) +cos^4 (θ +((3π)/4)).

$${simplify}\: \\ $$$${A}={cos}^{\mathrm{4}} \theta\:+{cos}^{\mathrm{4}} \left(\theta+\frac{\pi}{\mathrm{4}}\right)\:+{cos}^{\mathrm{4}} \left(\theta\:+\frac{\mathrm{2}\pi}{\mathrm{4}}\right)\:+{cos}^{\mathrm{4}} \left(\theta\:+\frac{\mathrm{3}\pi}{\mathrm{4}}\right). \\ $$

Question Number 28163    Answers: 0   Comments: 0

let give z= e^(i((2π)/(5 ))) and a= z +z^4 , b= z^2 +z^3 find a equation wich have a and for rootsthen find the values of cos(((2π)/(5)))), sin(((2π)/5)),cos(((4π)/5)) ,sin(((4π)/5)) ,cos((π/5)).

$${let}\:{give}\:{z}=\:{e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{5}\:}} \:\:\:\:{and}\:\:{a}=\:{z}\:+{z}^{\mathrm{4}} \:\:\:\:,\:\:\:{b}=\:{z}^{\mathrm{2}} +{z}^{\mathrm{3}} \\ $$$${find}\:{a}\:{equation}\:{wich}\:{have}\:{a}\:{and}\:{for}\:{rootsthen}\:{find} \\ $$$${the}\:{values}\:{of}\:{cos}\left(\frac{\mathrm{2}\pi}{\left.\mathrm{5}\right)}\right),\:{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right),{cos}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)\:,{sin}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)\:,{cos}\left(\frac{\pi}{\mathrm{5}}\right). \\ $$

Question Number 28162    Answers: 0   Comments: 1

find ∫_(1/2) ^2 (1+(1/x^2 ))arctanxdx.

$${find}\:\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{2}} \left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){arctanxdx}. \\ $$

Question Number 28161    Answers: 0   Comments: 0

find the value of ∫∫_W ln(1+x+y)dxdy with W={(x,y)∈R^2 / x+y≤1 and x≥0 and y≥0}.

$${find}\:{the}\:{value}\:{of}\:\int\int_{{W}} {ln}\left(\mathrm{1}+{x}+{y}\right){dxdy}\:{with} \\ $$$${W}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:{x}+{y}\leqslant\mathrm{1}\:{and}\:{x}\geqslant\mathrm{0}\:{and}\:{y}\geqslant\mathrm{0}\right\}. \\ $$

Question Number 28160    Answers: 0   Comments: 2

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

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

Question Number 28159    Answers: 0   Comments: 1

let give D=[0,(π/2)]×[0,(1/2)] find the value of ∫∫_D ((dxdy)/(ycosx +1)) .

$${let}\:{give}\:{D}=\left[\mathrm{0},\frac{\pi}{\mathrm{2}}\right]×\left[\mathrm{0},\frac{\mathrm{1}}{\mathrm{2}}\right]\:\:{find}\:{the}\:{value}\:{of} \\ $$$$\int\int_{{D}} \:\:\:\frac{{dxdy}}{{ycosx}\:+\mathrm{1}}\:\:. \\ $$

Question Number 28158    Answers: 1   Comments: 0

calculate ∫∫_(x^2 +y^2 ≤1) ((dxdy)/(3+x^2 +y^2 )) .

$${calculate}\:\int\int_{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant\mathrm{1}} \:\:\:\frac{{dxdy}}{\mathrm{3}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:\:. \\ $$

Question Number 28185    Answers: 1   Comments: 0

M, N are endpoints of a diameter 4x−y=15 of circle x^2 +y^2 −6x+6y−16=0 ; and are also on the tangents at the end points of the major axis of an ellipse respectively, such that MN is also tangent to the same ellipse at point P. If the major axis of the ellipse is along y=x, find eccentricity, length of latus rectum, centre and equation of derectrices.

$${M},\:{N}\:{are}\:{endpoints}\:{of}\:{a}\:{diameter} \\ $$$$\:\mathrm{4}{x}−{y}=\mathrm{15}\:\:{of}\:{circle} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{6}{y}−\mathrm{16}=\mathrm{0}\:;\:{and}\:{are} \\ $$$${also}\:{on}\:{the}\:{tangents}\:{at}\:{the}\:{end} \\ $$$${points}\:{of}\:{the}\:{major}\:{axis}\:{of}\:{an} \\ $$$${ellipse}\:{respectively},\:{such}\:{that} \\ $$$${MN}\:{is}\:{also}\:{tangent}\:{to}\:{the}\:{same} \\ $$$${ellipse}\:{at}\:{point}\:{P}. \\ $$$${If}\:{the}\:{major}\:{axis}\:{of}\:{the}\:{ellipse} \\ $$$${is}\:{along}\:{y}={x},\:{find} \\ $$$$\:\:\:{eccentricity},\:{length}\:{of}\:{latus} \\ $$$${rectum},\:{centre}\:{and}\:{equation}\:{of} \\ $$$${derectrices}. \\ $$

Question Number 28151    Answers: 0   Comments: 4

lim_(x→1) ((1/(log_e x)) − (x/(x − 1)))

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\:\left(\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{e}} \mathrm{x}}\:−\:\frac{\mathrm{x}}{\mathrm{x}\:−\:\mathrm{1}}\right) \\ $$

Question Number 28139    Answers: 1   Comments: 0

Question Number 28138    Answers: 0   Comments: 1

studie and?give the graph for the function f(x)= e^x −x^e .

$${studie}\:{and}?{give}\:{the}\:{graph}\:{for}\:{the}\:{function} \\ $$$${f}\left({x}\right)=\:{e}^{{x}} \:\:−{x}^{{e}} \:\:\:\:\:. \\ $$

Question Number 28202    Answers: 1   Comments: 1

Question Number 28201    Answers: 0   Comments: 0

prove the sine rule using dot product need help please

$$\mathrm{prove}\:\mathrm{the}\:\mathrm{sine}\:\mathrm{rule}\:\mathrm{using}\:\mathrm{dot}\:\mathrm{product} \\ $$$$\mathrm{need}\:\mathrm{help}\:\mathrm{please} \\ $$

Question Number 28143    Answers: 1   Comments: 0

x−(1/x)=3 x^2 −(1/x^2 )=?

$$\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}=\mathrm{3} \\ $$$$\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }=? \\ $$

Question Number 28124    Answers: 0   Comments: 3

f(R^+ →R) is a differentiable function obeying 2f(x)=f(xy)+f((x/y)) for all x,y ∈ R^+ and f(1)=0, f ′(1)=1 . Find f(x). More questions may follow..

$${f}\left({R}^{+} \rightarrow{R}\right)\:{is}\:{a}\:{differentiable} \\ $$$${function}\:{obeying} \\ $$$$\mathrm{2}{f}\left({x}\right)={f}\left({xy}\right)+{f}\left(\frac{{x}}{{y}}\right) \\ $$$${for}\:{all}\:{x},{y}\:\in\:{R}^{+} \:{and}\: \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{0},\:{f}\:'\left(\mathrm{1}\right)=\mathrm{1}\:. \\ $$$${Find}\:{f}\left({x}\right).\:{More}\:{questions}\:{may} \\ $$$${follow}.. \\ $$

Question Number 28116    Answers: 0   Comments: 0

Question Number 28105    Answers: 0   Comments: 1

Question Number 28098    Answers: 1   Comments: 0

lim_(x→∞) ((log_e x)/x^h ) , h > 0

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{log}_{\mathrm{e}} \mathrm{x}}{\mathrm{x}^{\mathrm{h}} }\:,\:\:\:\:\:\:\:\:\:\:\:\mathrm{h}\:>\:\mathrm{0} \\ $$

Question Number 28097    Answers: 0   Comments: 3

lim_(x→∞) ((3^x − 2^x )/x^2 )

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{3}^{\mathrm{x}} \:−\:\mathrm{2}^{\mathrm{x}} }{\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 28096    Answers: 0   Comments: 2

lim_(x→∞) (x^2 /(x − sinx))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{x}\:−\:\mathrm{sinx}} \\ $$

Question Number 28095    Answers: 0   Comments: 2

lim_(x→0^− ) (1 + tanx)^(−cotx)

$$\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\:\left(\mathrm{1}\:+\:\mathrm{tanx}\right)^{−\mathrm{cotx}} \\ $$

Question Number 28093    Answers: 0   Comments: 2

lim_(x→0^− ) (1 + tanx)^(cotx)

$$\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\:\left(\mathrm{1}\:+\:\mathrm{tanx}\right)^{\mathrm{cotx}} \\ $$

Question Number 28113    Answers: 1   Comments: 1

Question Number 28110    Answers: 0   Comments: 1

Question Number 28088    Answers: 0   Comments: 6

lim_(x→0^+ ) (sinx)^((tanx))

$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\:\left(\mathrm{sinx}\right)^{\left(\mathrm{tanx}\right)} \\ $$

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