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let give the sequence (u_n ) /u_0 =1 and u_1 =2 and ∀ n ∈N 2u_(n+2) =3 u_(n+1) −u_n . let give the sequence (v_n ) / v_n = u_(n+1) −u_n . 1) prove that (v_n ) is geometric .find v_n in terms of n 2) find u_n in terms of n.

$${let}\:{give}\:{the}\:{sequence}\:\left({u}_{{n}} \right)\:/{u}_{\mathrm{0}} =\mathrm{1}\:{and}\:{u}_{\mathrm{1}} =\mathrm{2}\:{and} \\ $$$$\forall\:{n}\:\in{N}\:\:\:\mathrm{2}{u}_{{n}+\mathrm{2}} =\mathrm{3}\:{u}_{{n}+\mathrm{1}} −{u}_{{n}} .\:{let}\:{give}\:{the}\:{sequence}\:\left({v}_{{n}} \right)\:/ \\ $$$${v}_{{n}} =\:{u}_{{n}+\mathrm{1}} −{u}_{{n}} \:. \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\left({v}_{{n}} \right)\:{is}\:{geometric}\:.{find}\:{v}_{{n}} {in}\:{terms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{u}_{{n}} \:{in}\:{terms}\:{of}\:{n}. \\ $$

Question Number 29140 Answers: 0 Comments: 6

Find no. of rational roots of f(x)= 2x^(98) +3x^(97) +2x^(96) +.....+2x+3=0.

$${Find}\:{no}.\:{of}\:{rational}\:{roots}\:{of}\:{f}\left({x}\right)= \\ $$$$\mathrm{2}{x}^{\mathrm{98}} +\mathrm{3}{x}^{\mathrm{97}} +\mathrm{2}{x}^{\mathrm{96}} +.....+\mathrm{2}{x}+\mathrm{3}=\mathrm{0}. \\ $$

Question Number 29138 Answers: 0 Comments: 4

Find number of polynomials p(x) with intgral coefficients such that p(1)=2, p(3)=1

$${Find}\:{number}\:{of}\:{polynomials}\:{p}\left({x}\right) \\ $$$${with}\:{intgral}\:{coefficients}\:{such}\:{that} \\ $$$${p}\left(\mathrm{1}\right)=\mathrm{2},\:{p}\left(\mathrm{3}\right)=\mathrm{1} \\ $$

Question Number 29134 Answers: 0 Comments: 3

Question Number 29131 Answers: 1 Comments: 2

If tan^2 atan^2 b+tan^2 btan^2 c+tan^2 ctan^2 a +2tan^2 atan^2 btan^2 c=1 then find the value of: sin^2 a+sin^2 b+sin^2 c

$${If}\:\mathrm{tan}^{\mathrm{2}} {a}\mathrm{tan}\:^{\mathrm{2}} {b}+\mathrm{tan}^{\mathrm{2}} {b}\mathrm{tan}\:^{\mathrm{2}} {c}+\mathrm{tan}^{\mathrm{2}} {c}\mathrm{tan}\:^{\mathrm{2}} {a} \\ $$$$+\mathrm{2tan}^{\mathrm{2}} {a}\mathrm{tan}^{\mathrm{2}} {b}\mathrm{tan}\:^{\mathrm{2}} {c}=\mathrm{1} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}: \\ $$$$\mathrm{sin}\:^{\mathrm{2}} {a}+\mathrm{sin}\:^{\mathrm{2}} {b}+\mathrm{sin}\:^{\mathrm{2}} {c} \\ $$

Question Number 29136 Answers: 0 Comments: 1

Question Number 29144 Answers: 1 Comments: 0

A body moves in a circular orbit of radius 4R round the earth. Express the acceleration of the free fall due to gravity of the body in terms of g R = radius if the earth g = acceleration due to gravity

$$\mathrm{A}\:\mathrm{body}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circular}\:\mathrm{orbit}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{4R}\:\mathrm{round}\:\mathrm{the}\:\mathrm{earth}.\:\:\mathrm{Express}\:\mathrm{the}\:\mathrm{acceleration} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{free}\:\mathrm{fall}\:\mathrm{due}\:\mathrm{to}\:\mathrm{gravity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{body}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{g} \\ $$$$\mathrm{R}\:=\:\mathrm{radius}\:\mathrm{if}\:\mathrm{the}\:\mathrm{earth} \\ $$$$\mathrm{g}\:=\:\mathrm{acceleration}\:\mathrm{due}\:\mathrm{to}\:\mathrm{gravity} \\ $$

Question Number 29159 Answers: 0 Comments: 1

let give f(x)=2(√(x−1)) +3x find f^(−1) (x) and (f^(−1) )^′ (x) .

$${let}\:{give}\:{f}\left({x}\right)=\mathrm{2}\sqrt{{x}−\mathrm{1}}\:+\mathrm{3}{x}\:\:\:{find}\:{f}^{−\mathrm{1}} \left({x}\right)\:{and}\:\left({f}^{−\mathrm{1}} \right)^{'} \left({x}\right)\:. \\ $$

Question Number 29158 Answers: 0 Comments: 1

find lim_(x→1) (((√(3+(√(2x−1)))) −2)/((√(2+(√(3x+1)))) −(√(x+3)))) .

$${find}\:{lim}_{{x}\rightarrow\mathrm{1}} \frac{\sqrt{\mathrm{3}+\sqrt{\mathrm{2}{x}−\mathrm{1}}}\:−\mathrm{2}}{\sqrt{\mathrm{2}+\sqrt{\mathrm{3}{x}+\mathrm{1}}}\:\:−\sqrt{{x}+\mathrm{3}}}\:\:. \\ $$

Question Number 29157 Answers: 1 Comments: 1

find lim_(x→1) (((x−2)^(1/3) +(1−x+x^2 )^(1/3) )/(x^2 −1)) .

$${find}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\:\frac{\left({x}−\mathrm{2}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \:\:+\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} }{{x}^{\mathrm{2}} −\mathrm{1}}\:. \\ $$

Question Number 29156 Answers: 0 Comments: 2

find lim_(x→0^+ ) x[(1/x)] and lim_(x→0^+ ) x^2 [ (1/x)] . [α] is the greatest integr inferior or equal to α.

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:\:{x}\left[\frac{\mathrm{1}}{{x}}\right]\:\:{and}\:\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:\:\:{x}^{\mathrm{2}} \:\left[\:\frac{\mathrm{1}}{{x}}\right]\:\:. \\ $$$$\left[\alpha\right]\:{is}\:{the}\:{greatest}\:{integr}\:{inferior}\:{or}\:{equal}\:{to}\:\alpha. \\ $$

Question Number 29123 Answers: 0 Comments: 0

Question Number 29118 Answers: 1 Comments: 6

Question Number 29116 Answers: 1 Comments: 0

Find the area of the region R bounded by the curve y = cosh(x), the line x = log_e (2) and the coordinate axis . Find also the volume obtained when R is rotated completely about the x − axis.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\:\boldsymbol{\mathrm{R}}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{curve}\:\:\mathrm{y}\:=\:\mathrm{cosh}\left(\mathrm{x}\right),\:\:\mathrm{the}\:\mathrm{line}\:\:\mathrm{x}\:=\:\mathrm{log}_{\mathrm{e}} \left(\mathrm{2}\right) \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{coordinate}\:\mathrm{axis}\:.\:\:\mathrm{Find}\:\mathrm{also}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{obtained}\:\mathrm{when}\:\boldsymbol{\mathrm{R}}\:\mathrm{is}\:\mathrm{rotated}\: \\ $$$$\mathrm{completely}\:\mathrm{about}\:\mathrm{the}\:\:\mathrm{x}\:−\:\mathrm{axis}. \\ $$

Question Number 29111 Answers: 1 Comments: 1

cos^3 x.sin^2 x=1/16(2cos x−cos 3x−cos 5x)

$$\mathrm{cos}^{\mathrm{3}} {x}.\mathrm{sin}\:^{\mathrm{2}} {x}=\mathrm{1}/\mathrm{16}\left(\mathrm{2cos}\:{x}−\mathrm{cos}\:\mathrm{3}{x}−\mathrm{cos}\:\mathrm{5}{x}\right) \\ $$

Question Number 29107 Answers: 1 Comments: 1

Question Number 29105 Answers: 0 Comments: 2

Show that: ∫_(−1) ^( 1) (dx/(5 cosh(x) + 13 sinh(x))) = (1/2) log_e (((15e − 10)/(3e + 2)))

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\int_{−\mathrm{1}} ^{\:\:\:\mathrm{1}} \:\:\:\:\:\:\:\frac{\mathrm{dx}}{\mathrm{5}\:\mathrm{cosh}\left(\mathrm{x}\right)\:+\:\mathrm{13}\:\mathrm{sinh}\left(\mathrm{x}\right)}\:\:=\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{log}_{\mathrm{e}} \left(\frac{\mathrm{15e}\:−\:\mathrm{10}}{\mathrm{3e}\:+\:\mathrm{2}}\right)\: \\ $$

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