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Question Number 57529 Answers: 0 Comments: 1

calculate Σ_(n=1) ^∞ (((−1)^n )/(n^3 (n+1)))

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{3}} \left({n}+\mathrm{1}\right)} \\ $$

Question Number 57525 Answers: 1 Comments: 0

Question Number 57522 Answers: 3 Comments: 3

The radius of circle having minimum area,which touches the curve y=4−x^2 and the lines y=∣x∣ is ?

$${The}\:{radius}\:{of}\:{circle}\:{having}\:{minimum} \\ $$$${area},{which}\:{touches}\:{the}\:{curve}\:{y}=\mathrm{4}−{x}^{\mathrm{2}} \\ $$$${and}\:{the}\:{lines}\:{y}=\mid{x}\mid\:{is}\:? \\ $$

Question Number 57521 Answers: 2 Comments: 1

Question Number 57515 Answers: 1 Comments: 4

Question Number 57513 Answers: 0 Comments: 4

There are 128 players in the first round of a knockout competition. Half of the players were knocked out in each round. How many players took part in the fourth round? How many rounds were there in this competion?

$$\mathrm{There}\:\mathrm{are}\:\mathrm{128}\:\mathrm{players}\:\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{round} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{knockout}\:\mathrm{competition}.\:\mathrm{Half}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{players}\:\mathrm{were}\:\mathrm{knocked}\:\mathrm{out}\:\mathrm{in}\:\mathrm{each}\:\mathrm{round}. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{players}\:\mathrm{took}\:\mathrm{part}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{fourth}\:\mathrm{round}?\:\mathrm{How}\:\mathrm{many}\:\mathrm{rounds}\:\mathrm{were}\:\mathrm{there} \\ $$$$\mathrm{in}\:\mathrm{this}\:\mathrm{competion}? \\ $$

Question Number 57494 Answers: 1 Comments: 1

Question Number 57491 Answers: 1 Comments: 0

If R is a region enclosed by y = f(x), y = g(x), x = a, x = b, is it possible to have f(x) and g(x) such that the center of gravity (x^ , y^ ) is not inside R ?

$$\mathrm{If}\:{R}\:\mathrm{is}\:\mathrm{a}\:\mathrm{region}\:\mathrm{enclosed}\:\mathrm{by}\:{y}\:=\:{f}\left({x}\right),\:{y}\:=\:{g}\left({x}\right),\:{x}\:=\:{a},\:{x}\:=\:{b}, \\ $$$$\mathrm{is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{have}\:{f}\left({x}\right)\:\mathrm{and}\:{g}\left({x}\right)\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{center}\:\mathrm{of}\:\mathrm{gravity}\:\left(\bar {{x}},\:\bar {{y}}\right)\:\mathrm{is}\:\mathrm{not}\:\mathrm{inside}\:{R}\:? \\ $$

Question Number 57490 Answers: 1 Comments: 2

1)findF(a)= ∫_0 ^∞ ((cos(ln(2+x^2 )))/(a^2 +x^2 ))dx witha>0 2) find the value of ∫_0 ^∞ ((cos(ln(2+x^2 )))/(4+x^2 ))dx.

$$\left.\mathrm{1}\right){findF}\left({a}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)\right)}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }{dx}\:\:{witha}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)\right)}{\mathrm{4}+{x}^{\mathrm{2}} }{dx}. \\ $$

Question Number 57489 Answers: 1 Comments: 1

find the value of Σ_(n=2) ^∞ ((3n^2 +1)/((n−1)^3 (n+1)^3 ))

$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\:\frac{\mathrm{3}{n}^{\mathrm{2}} \:+\mathrm{1}}{\left({n}−\mathrm{1}\right)^{\mathrm{3}} \left({n}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 57488 Answers: 1 Comments: 1

let A_n =∫_0 ^n ((t[t])/(3+t^2 ))dt 1)calculate lim_(n→+∞) A_n 2) find nature if Σ A_n

$${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{{n}} \:\:\:\frac{{t}\left[{t}\right]}{\mathrm{3}+{t}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right){calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{if}\:\Sigma\:{A}_{{n}} \\ $$

Question Number 57487 Answers: 0 Comments: 1

calculate lim_(x→1) ∫_x ^x^2 ((arctan(t))/(sint))dt .

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\:\:\frac{{arctan}\left({t}\right)}{{sint}}{dt}\:. \\ $$

Question Number 57486 Answers: 0 Comments: 4

let f(x) =((ln(1+x))/(2−x^2 )) 1)calculate f^((n)) (x) 2) calculate f^((n)) (0) 3)developp f(x) at integr serie.

$${let}\:{f}\left({x}\right)\:=\frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{2}−{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:\: \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right){developp}\:{f}\left({x}\right)\:{at}\:{integr}\:{serie}. \\ $$

Question Number 57480 Answers: 0 Comments: 2

if F(x,y)=F(y,x) and x+y=c (constant) prove that F_(max or min) =F((c/2),(c/2)).

$${if}\:{F}\left({x},{y}\right)={F}\left({y},{x}\right)\:{and}\:{x}+{y}={c}\:\left({constant}\right) \\ $$$${prove}\:{that}\:{F}_{{max}\:{or}\:{min}} ={F}\left(\frac{{c}}{\mathrm{2}},\frac{{c}}{\mathrm{2}}\right). \\ $$

Question Number 57474 Answers: 1 Comments: 2

prove sin18×cos36=(1/4)

$$\mathrm{prove}\: \\ $$$$\boldsymbol{{sin}}\mathrm{18}×\boldsymbol{{cos}}\mathrm{36}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 57469 Answers: 0 Comments: 3

((4tan75)/(1−tan^2 75))=(1/(cos150)) find tan75 in surd form

$$\frac{\mathrm{4}{tan}\mathrm{75}}{\mathrm{1}−{tan}^{\mathrm{2}} \mathrm{75}}=\frac{\mathrm{1}}{{cos}\mathrm{150}}\: \\ $$$${find}\:{tan}\mathrm{75}\:{in}\:{surd}\:{form} \\ $$

Question Number 57462 Answers: 0 Comments: 0

Two conductors has total charge of +10.0μC and −10μC with 10volt between them. (a) Determine the capacitance between them (b) what is the p.d between the two condoctors if the charge on each are increased to +100μC and −100μC respectively ?

$$\mathrm{Two}\:\mathrm{conductors}\:\mathrm{has}\:\mathrm{total}\:\mathrm{charge}\:\mathrm{of} \\ $$$$+\mathrm{10}.\mathrm{0}\mu\mathrm{C}\:\mathrm{and}\:−\mathrm{10}\mu\mathrm{C}\:\mathrm{with}\:\mathrm{10volt}\: \\ $$$$\mathrm{between}\:\mathrm{them}. \\ $$$$\:\left(\mathrm{a}\right)\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{capacitance}\:\mathrm{between}\:\mathrm{them} \\ $$$$\:\left(\mathrm{b}\right)\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{p}.\mathrm{d}\:\mathrm{between}\:\mathrm{the}\:\mathrm{two} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{condoctors}\:\mathrm{if}\:\mathrm{the}\:\mathrm{charge}\:\mathrm{on}\:\mathrm{each} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{are}\:\mathrm{increased}\:\mathrm{to}\:+\mathrm{100}\mu\mathrm{C}\:\mathrm{and}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:−\mathrm{100}\mu\mathrm{C}\:\mathrm{respectively}\:? \\ $$

Question Number 57456 Answers: 0 Comments: 0