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Question Number 165089 Answers: 0 Comments: 0

Question Number 165081 Answers: 1 Comments: 0

Given a; b >0 and ∀ n ∈ N, u_n ;v_n >0 . { ((u_0 =a)),((u_(n+1) =(√(u_n v_n )))) :} and { ((v_0 =b)),((v_(n+1) =(1/2)(u_n +v_n ).)) :} Show that the sequences u_n and u_n are convergent and have the same limit l (l is called the arithmetico−geometric limit).

$${Given}\:{a};\:{b}\:>\mathrm{0}\:{and}\:\forall\:{n}\:\in\:\mathbb{N},\:{u}_{{n}} ;{v}_{{n}} >\mathrm{0}\:. \\ $$$$\:\begin{cases}{{u}_{\mathrm{0}} ={a}}\\{{u}_{{n}+\mathrm{1}} =\sqrt{{u}_{{n}} {v}_{{n}} }}\end{cases}\:{and}\:\begin{cases}{{v}_{\mathrm{0}} ={b}}\\{{v}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}\left({u}_{{n}} +{v}_{{n}} \right).}\end{cases} \\ $$$${Show}\:{that}\:{the}\:{sequences}\:{u}_{{n}} \:{and}\:{u}_{{n}} \\ $$$${are}\:{convergent}\:{and}\:{have}\:{the}\:{same} \\ $$$${limit}\:{l}\:\left({l}\:{is}\:{called}\:{the}\:{arithmetico}−{geometric}\:{limit}\right). \\ $$

Question Number 165073 Answers: 0 Comments: 0

Question Number 165072 Answers: 0 Comments: 14

prove speed of sound in air v=331+0.6Tc^° ((m/(sec)))

$${prove}\:{speed}\:{of}\:{sound}\:{in}\:{air} \\ $$$${v}=\mathrm{331}+\mathrm{0}.\mathrm{6}{Tc}^{°} \left(\frac{{m}}{{sec}}\right) \\ $$

Question Number 165070 Answers: 1 Comments: 0

Question Number 165068 Answers: 0 Comments: 1

Question Number 165063 Answers: 1 Comments: 1

lim_(x→0) ((x^(tanx) −cosx)/(x^(sinx) −e^x ))

$$\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{x}^{{tanx}} −{cosx}}{{x}^{{sinx}} −{e}^{{x}} } \\ $$

Question Number 165057 Answers: 1 Comments: 1

Question Number 165054 Answers: 1 Comments: 0

Question Number 165060 Answers: 1 Comments: 0

x−(1/x)=4 then x^2 −(1/x^2 )=?

$${x}−\frac{\mathrm{1}}{{x}}=\mathrm{4}\:\:{then}\:{x}^{\mathrm{2}} −\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=? \\ $$

Question Number 165044 Answers: 0 Comments: 2

If n = j + k, prove or disprove (d^n /dx^n )f(x) = (d^j /dx^j )((d^k /dx^k )f(x)) = (d^k /dx^k )((d^j /dx^j )f(x))

$$\mathrm{If}\:{n}\:=\:{j}\:+\:{k},\:\mathrm{prove}\:\mathrm{or}\:\mathrm{disprove} \\ $$$$\frac{{d}^{{n}} }{{dx}^{{n}} }{f}\left({x}\right)\:=\:\frac{{d}^{{j}} }{{dx}^{{j}} }\left(\frac{{d}^{{k}} }{{dx}^{{k}} }{f}\left({x}\right)\right)\:=\:\frac{{d}^{{k}} }{{dx}^{{k}} }\left(\frac{{d}^{{j}} }{{dx}^{{j}} }{f}\left({x}\right)\right) \\ $$

Question Number 165010 Answers: 0 Comments: 0

Ω= Σ_(n=1) ^∞ (( ψ^((2)) ( 1+ n ))/( n)) = ? −−− m.n −−−

$$ \\ $$$$\:\:\:\:\:\:\:\Omega=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\psi\:^{\left(\mathrm{2}\right)} \left(\:\mathrm{1}+\:{n}\:\right)}{\:{n}}\:=\:? \\ $$$$\:\:\:\:\:\:−−−\:{m}.{n}\:−−− \\ $$$$\:\:\:\: \\ $$

Question Number 165006 Answers: 0 Comments: 1

Question Number 165024 Answers: 1 Comments: 7

Question Number 165021 Answers: 2 Comments: 0

fog=6x^2 −2x+3 gof=12x^2 −14x+6 f(2)=?

$${fog}=\mathrm{6}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{3} \\ $$$${gof}=\mathrm{12}{x}^{\mathrm{2}} −\mathrm{14}{x}+\mathrm{6} \\ $$$${f}\left(\mathrm{2}\right)=? \\ $$

Question Number 165019 Answers: 0 Comments: 0

Question Number 165018 Answers: 0 Comments: 0

y = Γ(m+n) Find (dy/dn)

$${y}\:=\:\Gamma\left({m}+{n}\right)\: \\ $$$${Find}\:\frac{{dy}}{{dn}} \\ $$

Question Number 165017 Answers: 0 Comments: 0

Question Number 165015 Answers: 2 Comments: 2

Question Number 164996 Answers: 1 Comments: 0

Question Number 164995 Answers: 1 Comments: 0

Question Number 164993 Answers: 1 Comments: 0

solve by series ∫_0 ^( ∞) ((sinx)/x) dx

$${solve}\:{by}\:{series}\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{sinx}}{{x}}\:{dx} \\ $$

Question Number 164992 Answers: 0 Comments: 0

Question Number 164991 Answers: 2 Comments: 1

Solve by resideo theorem ∫_(−∞) ^( ∞) (z^2 /(z^4 +1)) dz

$$\boldsymbol{{Solve}}\:\boldsymbol{{by}}\:\boldsymbol{{resideo}}\:\boldsymbol{{theorem}}\:\int_{−\infty} ^{\:\infty} \:\frac{\boldsymbol{{z}}^{\mathrm{2}} }{\boldsymbol{{z}}^{\mathrm{4}} +\mathrm{1}}\:\boldsymbol{{dz}} \\ $$

Question Number 164985 Answers: 2 Comments: 0

Question Number 164982 Answers: 0 Comments: 0

Prove, that (a/b) : (c/d) = (a/b) ∙ (d/c)

$$\mathrm{Prove},\:\mathrm{that}\:\frac{{a}}{{b}}\::\:\frac{{c}}{{d}}\:=\:\frac{{a}}{{b}}\:\centerdot\:\frac{{d}}{{c}} \\ $$

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