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Question Number 167853 Answers: 1 Comments: 0

Par de^ velopement limite^ lim_(x→0) ((ln (1+x)−sin x)/( (√(1+x^2 ))−cos x^2 ))

$${Par}\:{d}\acute {{e}velopement}\:{limit}\acute {{e}} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{ln}\:\left(\mathrm{1}+{x}\right)−\mathrm{sin}\:{x}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }−\mathrm{cos}\:{x}^{\mathrm{2}} } \\ $$

Question Number 167851 Answers: 1 Comments: 0

A particular A.P has a positive common difference and is such that for any three adjacent terms, three times the sum of their squares exceed the square of their sum by 37.5 . Find the common difference.

$$\:\:\mathrm{A}\:\mathrm{particular}\:\mathrm{A}.\mathrm{P}\:\mathrm{has}\:\mathrm{a}\:\mathrm{positive}\: \\ $$$$\:\:\mathrm{common}\:\mathrm{difference}\:\mathrm{and}\:\mathrm{is}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\mathrm{for}\:\mathrm{any}\:\mathrm{three}\:\mathrm{adjacent}\:\mathrm{terms},\:\mathrm{three} \\ $$$$\:\mathrm{times}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{squares}\:\mathrm{exceed} \\ $$$$\:\mathrm{the}\:\mathrm{square}\:\mathrm{of}\:\mathrm{their}\:\mathrm{sum}\:\mathrm{by}\:\mathrm{37}.\mathrm{5}\:.\:\mathrm{Find} \\ $$$$\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}.\: \\ $$

Question Number 167848 Answers: 0 Comments: 0

Dans une PME, sont employes 6ouvriers 5 employes. le PDG souhaite prendre l′avis de son personnel. il interroge 7 personnes choisies au hasard parmi ces 11 personnes. soit X la variable aleatoire: “nombre d′ouvriers interroges” 1)quelles sont les valeurs prises par X 2)quelle est la loi de probabilite 3)calculons la probabilite d′interroger 4 ouvrier

$${Dans}\:{une}\:{PME},\:{sont}\:{employes}\:\mathrm{6}{ouvriers} \\ $$$$\mathrm{5}\:{employes}.\:{le}\:{PDG}\:{souhaite}\:{prendre}\:{l}'{avis} \\ $$$${de}\:{son}\:{personnel}.\:{il}\:{interroge}\:\mathrm{7}\:{personnes} \\ $$$${choisies}\:{au}\:{hasard}\:{parmi}\:{ces}\:\mathrm{11}\:{personnes}. \\ $$$${soit}\:{X}\:{la}\:{variable}\:{aleatoire}:\:``{nombre}\: \\ $$$${d}'{ouvriers}\:{interroges}'' \\ $$$$\left.\mathrm{1}\right){quelles}\:{sont}\:{les}\:{valeurs}\:{prises}\:{par}\:{X} \\ $$$$\left.\mathrm{2}\right){quelle}\:{est}\:{la}\:{loi}\:{de}\:{probabilite} \\ $$$$\left.\mathrm{3}\right){calculons}\:{la}\:{probabilite}\:{d}'{interroger}\:\mathrm{4} \\ $$$${ouvrier} \\ $$

Question Number 167840 Answers: 0 Comments: 1

Question Number 167839 Answers: 1 Comments: 0

Question Number 167838 Answers: 1 Comments: 0

(dy/dx)=8x+4y+(2x+y−1)^2 y=?

$$\:\:\:\:\:\:\frac{{dy}}{{dx}}=\mathrm{8}{x}+\mathrm{4}{y}+\left(\mathrm{2}{x}+{y}−\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:{y}=? \\ $$

Question Number 167830 Answers: 0 Comments: 1

Question Number 167828 Answers: 1 Comments: 0

Houses on one side of a particular street are assigned odd numbers, starting from 11. If the sum of the numbers is 551, how many houses are there?

$$\:\mathrm{Houses}\:\mathrm{on}\:\mathrm{one}\:\mathrm{side}\:\mathrm{of}\:\mathrm{a}\:\mathrm{particular}\: \\ $$$$\:\mathrm{street}\:\mathrm{are}\:\mathrm{assigned}\:\mathrm{odd}\:\mathrm{numbers},\: \\ $$$$\:\mathrm{starting}\:\mathrm{from}\:\mathrm{11}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{551},\:\mathrm{how}\:\mathrm{many}\:\mathrm{houses} \\ $$$$\:\mathrm{are}\:\mathrm{there}? \\ $$

Question Number 167823 Answers: 1 Comments: 2

Question Number 167821 Answers: 0 Comments: 2

Question Number 167820 Answers: 1 Comments: 0

given x^2 =(π^2 /3)+4Σ(−1)^n ((cos(nx))/n^2 ), show that Σ(1/((2n−1)^2 ))=(π^2 /8)

$$\mathrm{given}\:\:\mathrm{x}^{\mathrm{2}} =\frac{\pi^{\mathrm{2}} }{\mathrm{3}}+\mathrm{4}\Sigma\left(−\mathrm{1}\right)^{\mathrm{n}} \frac{\mathrm{cos}\left(\mathrm{nx}\right)}{\mathrm{n}^{\mathrm{2}} },\:\mathrm{show}\:\mathrm{that}\:\Sigma\frac{\mathrm{1}}{\left(\mathrm{2n}−\mathrm{1}\right)^{\mathrm{2}} }=\frac{\pi^{\mathrm{2}} }{\mathrm{8}} \\ $$

Question Number 167819 Answers: 0 Comments: 0

let f(x)=e^(−x) arctan(2x) find f^((n)) (0)

$${let}\:{f}\left({x}\right)={e}^{−{x}} {arctan}\left(\mathrm{2}{x}\right) \\ $$$${find}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$

Question Number 167800 Answers: 0 Comments: 3

5^(2x) = 2.10^x −4^(2x) (((x−4)^(x^2 +2) ))^(1/((x+2)^(−1) )) =?

$$\:\:\:\:\:\:\mathrm{5}^{\mathrm{2}{x}} \:=\:\mathrm{2}.\mathrm{10}^{{x}} −\mathrm{4}^{\mathrm{2}{x}} \: \\ $$$$\:\:\:\:\:\sqrt[{\left({x}+\mathrm{2}\right)^{−\mathrm{1}} }]{\left({x}−\mathrm{4}\right)^{{x}^{\mathrm{2}} +\mathrm{2}} }=?\: \\ $$

Question Number 167795 Answers: 2 Comments: 1

Question Number 167787 Answers: 2 Comments: 0

Question Number 167785 Answers: 0 Comments: 0

Question Number 167784 Answers: 0 Comments: 0

Question Number 167782 Answers: 1 Comments: 0

etudier l′existance de limite en (0,0) f(x,y)=((x^2 y)/(x+y))

$${etudier}\:{l}'{existance}\:{de}\:{limite}\:{en}\:\left(\mathrm{0},\mathrm{0}\right) \\ $$$${f}\left({x},{y}\right)=\frac{{x}^{\mathrm{2}} {y}}{{x}+{y}} \\ $$

Question Number 167808 Answers: 1 Comments: 1

Question Number 167777 Answers: 1 Comments: 0

Question Number 167776 Answers: 2 Comments: 0

Question Number 167775 Answers: 1 Comments: 1

Question Number 167765 Answers: 0 Comments: 0

show that two permutations are conjugate if their matrices are similar

$$ \\ $$show that two permutations are conjugate if their matrices are similar

Question Number 167773 Answers: 2 Comments: 0

Calculate ∫((xtan x)/(cos^4 x))dx

$${Calculate} \\ $$$$\int\frac{{x}\mathrm{tan}\:{x}}{\mathrm{cos}\:^{\mathrm{4}} {x}}{dx} \\ $$

Question Number 167757 Answers: 1 Comments: 1

Calculate ∫sec^2 xsec xdx

$${Calculate} \\ $$$$\int\mathrm{sec}\:^{\mathrm{2}} {x}\mathrm{sec}\:{xdx} \\ $$

Question Number 167746 Answers: 1 Comments: 1

log_((x^2 +2)) (x^2 +4x)=?

$${log}_{\left({x}^{\mathrm{2}} +\mathrm{2}\right)} \left({x}^{\mathrm{2}} +\mathrm{4}{x}\right)=? \\ $$

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