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Question Number 165270 Answers: 2 Comments: 0

Question Number 165157 Answers: 2 Comments: 1

Σ_(k=6) ^(n+6) (k−4)=((an^2 +bn+c)/2) a+b+c=?

$$\underset{{k}=\mathrm{6}} {\overset{{n}+\mathrm{6}} {\sum}}\left({k}−\mathrm{4}\right)=\frac{{an}^{\mathrm{2}} +{bn}+{c}}{\mathrm{2}} \\ $$$${a}+{b}+{c}=? \\ $$

Question Number 165273 Answers: 1 Comments: 0

lim_( n→ ∞) ∫_0 ^( 1) (( n . e^( 1− x^( 2) ) )/( 1 + n^( 2) x^( 2) )) dx =? −−−−−−

$$ \\ $$$$\:\:\:\:\:\:{lim}_{\:{n}\rightarrow\:\infty} \:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\:{n}\:.\:{e}^{\:\mathrm{1}−\:{x}^{\:\mathrm{2}} } }{\:\mathrm{1}\:+\:{n}^{\:\mathrm{2}} \:{x}^{\:\mathrm{2}} }\:{dx}\:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:−−−−−− \\ $$

Question Number 165272 Answers: 2 Comments: 0

Question Number 165153 Answers: 3 Comments: 0

f(x)=3e^(2x) f^(−1) (x)=?

$${f}\left({x}\right)=\mathrm{3}{e}^{\mathrm{2}{x}} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=? \\ $$

Question Number 165152 Answers: 1 Comments: 0

prove Ω=∫_0 ^( 1) (( x − x^( 2) )/((1+x )ln(x))) dx = ln((4/π) ) −−−−−

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{prove} \\ $$$$\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{x}\:−\:{x}^{\:\mathrm{2}} }{\left(\mathrm{1}+{x}\:\right){ln}\left({x}\right)}\:{dx}\:=\:{ln}\left(\frac{\mathrm{4}}{\pi}\:\right) \\ $$$$\:\:\:−−−−− \\ $$

Question Number 165122 Answers: 1 Comments: 3

Question Number 165119 Answers: 0 Comments: 1

Question Number 165107 Answers: 1 Comments: 8

does it also happen to you? when i try to refresh with “↻”, it shows following message:

$${does}\:{it}\:{also}\:{happen}\:{to}\:{you}? \\ $$$${when}\:{i}\:{try}\:{to}\:{refresh}\:{with}\:``\circlearrowright'',\:{it} \\ $$$${shows}\:{following}\:{message}: \\ $$

Question Number 165099 Answers: 2 Comments: 1

the rest of the division euclidienne of 10^(99) by 13×17 is?

$$\:{the}\:{rest}\:{of}\:{the}\:{division}\:{euclidienne}\:{of} \\ $$$$\mathrm{10}^{\mathrm{99}} \:\:{by}\:\:\mathrm{13}×\mathrm{17}\:{is}? \\ $$

Question Number 165098 Answers: 2 Comments: 0

Question Number 165097 Answers: 1 Comments: 0

Question Number 165094 Answers: 0 Comments: 0

Question Number 165093 Answers: 1 Comments: 2

x^(lim) →3(2x+3x−4) FAILED TO CALCULATE

$$\overset{{lim}} {{x}}\rightarrow\mathrm{3}\left(\mathrm{2}{x}+\mathrm{3}{x}−\mathrm{4}\right) \\ $$$$\mathrm{FAILED}\:\mathrm{TO}\:\mathrm{CALCULATE} \\ $$

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