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AllQuestion and Answers: Page 251

Question Number 194967 Answers: 1 Comments: 0

Question Number 194963 Answers: 2 Comments: 0

Question Number 194961 Answers: 1 Comments: 0

Question Number 194960 Answers: 1 Comments: 0

Soit x>1. On de^ finie la suite (p_n ) par p_1 =x et ∀n∈IN^∗ p_(n+1) =2p_n ^2 −1 Montrer que lim_(n→+∞) Π_(k=1) ^n (1+(1/p_k ))=(√((x+1)/(x−1)))

$$\mathrm{Soit}\:{x}>\mathrm{1}.\:\mathrm{On}\:\mathrm{d}\acute {\mathrm{e}finie}\:\mathrm{la}\:\mathrm{suite}\:\left(\mathrm{p}_{\mathrm{n}} \right)\:\mathrm{par}\: \\ $$$$\mathrm{p}_{\mathrm{1}} ={x}\:\:\mathrm{et}\:\forall\mathrm{n}\in\mathrm{IN}^{\ast} \:\:\:\:\:\mathrm{p}_{\mathrm{n}+\mathrm{1}} =\mathrm{2p}_{\mathrm{n}} ^{\mathrm{2}} −\mathrm{1} \\ $$$$\mathrm{Montrer}\:\mathrm{que}\:\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{p}_{\mathrm{k}} }\right)=\sqrt{\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}} \\ $$

Question Number 194975 Answers: 0 Comments: 6

∫(1/(x^5 +1))dx

$$\int\frac{\mathrm{1}}{\boldsymbol{{x}}^{\mathrm{5}} +\mathrm{1}}\boldsymbol{{dx}} \\ $$

Question Number 194953 Answers: 1 Comments: 0

Let P(x)= x^2 +(x/2)+b and Q(x)=x^2 +cx+d be two polynomial with real coefficients such that P(x)Q(x)= Q(P(x)) for all real x . Find all the real roots of P(Q(x))=0

$$\:{Let}\:{P}\left({x}\right)=\:{x}^{\mathrm{2}} +\frac{{x}}{\mathrm{2}}+{b}\:{and} \\ $$$$\:\:{Q}\left({x}\right)={x}^{\mathrm{2}} +{cx}+{d}\:{be}\:{two}\: \\ $$$$\:\:{polynomial}\:{with}\:{real}\:{coefficients} \\ $$$$\:\:{such}\:{that}\:{P}\left({x}\right){Q}\left({x}\right)=\:{Q}\left({P}\left({x}\right)\right) \\ $$$$\:{for}\:{all}\:{real}\:{x}\:. \\ $$$$\:\:{Find}\:{all}\:{the}\:{real}\:{roots}\:{of}\: \\ $$$$\:\:{P}\left({Q}\left({x}\right)\right)=\mathrm{0}\: \\ $$

Question Number 194952 Answers: 1 Comments: 0

x + (√(17−x^2 )) + x(√(17−x^2 )) =9 find the possible value of X

$$\boldsymbol{\mathrm{x}}\:+\:\sqrt{\mathrm{17}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\:\:+\:\boldsymbol{\mathrm{x}}\sqrt{\mathrm{17}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:}\:=\mathrm{9} \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{possible}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{X}} \\ $$

Question Number 194942 Answers: 2 Comments: 2

$$\:\:\:\:\: \\ $$

Question Number 194939 Answers: 0 Comments: 0

Question Number 194938 Answers: 0 Comments: 0

Question Number 194937 Answers: 1 Comments: 0

If tan ((π/(24)))= ((√a)−(√b))((√c)−(√d)) where a,b,c,d are postive numbers. Find the value of (a+b+c+d+2)

$$\:\:{If}\:\mathrm{tan}\:\left(\frac{\pi}{\mathrm{24}}\right)=\:\left(\sqrt{{a}}−\sqrt{{b}}\right)\left(\sqrt{{c}}−\sqrt{{d}}\right) \\ $$$$\:\:{where}\:{a},{b},{c},{d}\:{are}\:{postive}\:{numbers}. \\ $$$$\:\:{Find}\:{the}\:{value}\:{of}\:\left({a}+{b}+{c}+{d}+\mathrm{2}\right) \\ $$

Question Number 194931 Answers: 2 Comments: 0

Question Number 194930 Answers: 0 Comments: 1

∫_0 ^1 x^(−x) dx=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{−{x}} {dx}=? \\ $$

Question Number 194928 Answers: 1 Comments: 0

lim_(x→∞) ((√(x^2 +5x+1)) +(√(x^2 −2x+1))+(√(x^2 +3))+(√(x^2 −4x+9))−(√(16x^2 −8)) =?

$$\:\:\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{1}}\:+\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}}+\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}+\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{9}}−\sqrt{\mathrm{16}{x}^{\mathrm{2}} −\mathrm{8}}\:=?\right. \\ $$

Question Number 194903 Answers: 1 Comments: 1

Question Number 194915 Answers: 2 Comments: 4

(3/(x−3))+(5/(x−5))+(7/(x−17))+((19)/(x−19))=x^2 −11x−4

$$ \\ $$$$\frac{\mathrm{3}}{{x}−\mathrm{3}}+\frac{\mathrm{5}}{{x}−\mathrm{5}}+\frac{\mathrm{7}}{{x}−\mathrm{17}}+\frac{\mathrm{19}}{{x}−\mathrm{19}}={x}^{\mathrm{2}} −\mathrm{11}{x}−\mathrm{4} \\ $$

Question Number 194914 Answers: 2 Comments: 0

Question Number 194913 Answers: 2 Comments: 0

Question Number 194899 Answers: 1 Comments: 0

Question Number 194900 Answers: 1 Comments: 0

Given d = (((2+ (√5)))^(1/3) /(1+(√5))) then d^3 −4d^2 +8d −2 =?

$$\:\:\:\:\:\:{Given}\:\:\:{d}\:=\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{2}+\:\sqrt{\mathrm{5}}}}{\mathrm{1}+\sqrt{\mathrm{5}}}\:\: \\ $$$$\:\:\:\:\:\:{then}\:\:{d}^{\mathrm{3}} −\mathrm{4}{d}^{\mathrm{2}} \:+\mathrm{8}{d}\:−\mathrm{2}\:=?\: \\ $$$$\:\:\:\:\: \\ $$

Question Number 194896 Answers: 1 Comments: 0

$$\:\:\:\:\:\:\:\cancel{ } \\ $$

Question Number 194891 Answers: 1 Comments: 0

lim_(x→3^+ ) ((((√x)−(√(x−3))−(√3))/( (√(x^2 −9)))) )=?

$$\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{3}^{+} } {\mathrm{lim}}\:\left(\frac{\sqrt{{x}}−\sqrt{{x}−\mathrm{3}}−\sqrt{\mathrm{3}}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{9}}}\:\right)=? \\ $$

Question Number 194888 Answers: 1 Comments: 0

Question Number 194887 Answers: 1 Comments: 0

What is the Inverse laplace transform of ((S + 2)/(S^2 +4S + 7)) Urgent!

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{Inverse}\:\mathrm{laplace}\:\mathrm{transform}\:\mathrm{of} \\ $$$$\frac{\mathrm{S}\:+\:\mathrm{2}}{\mathrm{S}^{\mathrm{2}} \:+\mathrm{4S}\:+\:\mathrm{7}} \\ $$$$ \\ $$$$\mathrm{Urgent}! \\ $$

Question Number 194881 Answers: 1 Comments: 0

Give △ABC Proof: sin A + sin B + sin C > 2

$${Give}\:\bigtriangleup{ABC}\: \\ $$$${Proof}:\:{sin}\:{A}\:+\:{sin}\:{B}\:+\:{sin}\:{C}\:>\:\mathrm{2} \\ $$

Question Number 194884 Answers: 1 Comments: 0

x! = 6!. 7! x^2 =?

$$\:\:\:\:\:\:{x}!\:=\:\mathrm{6}!.\:\mathrm{7}!\: \\ $$$$\:\:\:\:\:\:{x}^{\mathrm{2}} \:=?\: \\ $$

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