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AllQuestion and Answers: Page 589

Question Number 160981 Answers: 0 Comments: 1

Question Number 160980 Answers: 2 Comments: 0

How many ways can 50 people be divided into 3 groups, so that each group contains members equal to a prime number?

$$\:\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{50}\:\mathrm{people} \\ $$$$\:\mathrm{be}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{3}\:\mathrm{groups},\:\mathrm{so} \\ $$$$\:\mathrm{that}\:\mathrm{each}\:\mathrm{group}\:\mathrm{contains}\:\mathrm{members} \\ $$$$\:\mathrm{equal}\:\mathrm{to}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}? \\ $$

Question Number 160979 Answers: 1 Comments: 0

Ω=∫_0 ^1 x^(n−1) ln(1−x)dx=??? n≥1

$$\Omega=\int_{\mathrm{0}} ^{\mathrm{1}} \boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{n}}−\mathrm{1}} \boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{dx}}=???\:\:\: \\ $$$$\boldsymbol{\mathrm{n}}\geqslant\mathrm{1} \\ $$

Question Number 160976 Answers: 2 Comments: 0

Question Number 160970 Answers: 1 Comments: 0

there are even number divided all odd number what is the number ?

$${there}\:{are}\:{even}\:{number}\:{divided}\:{all}\:{odd} \\ $$$${number}\:{what}\:{is}\:{the}\:{number}\:? \\ $$

Question Number 160969 Answers: 1 Comments: 0

∫_(−2) ^( 2) x^3 cos((x/2)) (√(4−x^2 )) dx

$$\int_{−\mathrm{2}} ^{\:\mathrm{2}} {x}^{\mathrm{3}} {cos}\left(\frac{{x}}{\mathrm{2}}\right)\:\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }\:{dx} \\ $$

Question Number 160968 Answers: 1 Comments: 0

Question Number 160967 Answers: 0 Comments: 0

Question Number 161015 Answers: 2 Comments: 1

Question Number 161014 Answers: 0 Comments: 0

Question Number 160953 Answers: 1 Comments: 0

∫_o ^(+oo) ((tlnt)/((1+t)^2 )) etudier la convergence

$$\int_{{o}} ^{+{oo}} \:\frac{{tlnt}}{\left(\mathrm{1}+{t}\right)^{\mathrm{2}} }\:\:\:\: \\ $$$${etudier}\:{la}\:{convergence} \\ $$

Question Number 160950 Answers: 1 Comments: 0

Question Number 160949 Answers: 0 Comments: 0

Question Number 160948 Answers: 1 Comments: 0

(1/(1∙2))+(1/(3∙4))+(1/(5∙6))+...+(1/(39∙40))=?

$$\frac{\mathrm{1}}{\mathrm{1}\centerdot\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}\centerdot\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}\centerdot\mathrm{6}}+...+\frac{\mathrm{1}}{\mathrm{39}\centerdot\mathrm{40}}=? \\ $$

Question Number 160939 Answers: 2 Comments: 1

logx_(ab) =? if logx_a =30 andlogx_b =70

$${log}\underset{{ab}} {{x}}=?\:\:\:\:\:\:{if}\:\:{log}\underset{{a}} {{x}}=\mathrm{30}\:\:{andlog}\underset{{b}} {{x}}=\mathrm{70} \\ $$

Question Number 160938 Answers: 1 Comments: 0

lim_(x→(π/2)) ((π/(cos x)) −2x tan x )=?

$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\left(\frac{\pi}{\mathrm{cos}\:\mathrm{x}}\:−\mathrm{2x}\:\mathrm{tan}\:\mathrm{x}\:\right)=? \\ $$

Question Number 160937 Answers: 1 Comments: 0

lim_(x→∞) ( sin (√(x^2 +1))−sin (√(x^2 −1)) )=?

$$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\:\mathrm{sin}\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}−\mathrm{sin}\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}\:\right)=? \\ $$

Question Number 160933 Answers: 1 Comments: 0

In the given equation below , applying the formula for the derivative of inverse trigonometric functions , what is the ′′u ′′ from the given function. y = cosec^(−1) [ sin (((1+sin x)/(cos x)))]

$$\:{In}\:{the}\:{given}\:{equation}\:{below}\:,\:{applying} \\ $$$${the}\:{formula}\:{for}\:{the}\:{derivative}\:{of} \\ $$$$\:{inverse}\:{trigonometric}\:{functions}\:, \\ $$$$\:{what}\:{is}\:{the}\:''{u}\:''\:{from}\:{the}\:{given}\:{function}. \\ $$$$\:{y}\:=\:\mathrm{cosec}^{−\mathrm{1}} \left[\:\mathrm{sin}\:\left(\frac{\mathrm{1}+\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}\right)\right] \\ $$

Question Number 160931 Answers: 1 Comments: 0

x = 2^(log _5 (x+3)) ; x=?

$$\:\:{x}\:=\:\mathrm{2}^{\mathrm{log}\:_{\mathrm{5}} \left({x}+\mathrm{3}\right)} \:;\:{x}=? \\ $$

Question Number 160928 Answers: 1 Comments: 0

calculate Ω = Σ_(n=1) ^∞ (( ζ ( 1+ n ) −1)/(n + 1)) =^? 1− γ −−−−−−−−−−−

$$ \\ $$$$\:\:\:\:\:\:\:{calculate} \\ $$$$ \\ $$$$\:\:\:\:\Omega\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\zeta\:\left(\:\mathrm{1}+\:{n}\:\right)\:−\mathrm{1}}{{n}\:+\:\mathrm{1}}\:\overset{?} {=}\:\mathrm{1}−\:\gamma\: \\ $$$$\:−−−−−−−−−−− \\ $$

Question Number 160924 Answers: 1 Comments: 1

Question Number 160923 Answers: 0 Comments: 1

{ (((x+y)^(2021) = z)),(((x+z)^(2021) = y)),(((y+z)^(2021) = x)) :} (x,y,z)=...

$$\:\:\begin{cases}{\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2021}} =\:\mathrm{z}}\\{\left(\mathrm{x}+\mathrm{z}\right)^{\mathrm{2021}} \:=\:\mathrm{y}}\\{\left(\mathrm{y}+\mathrm{z}\right)^{\mathrm{2021}} \:=\:\mathrm{x}}\end{cases} \\ $$$$\:\:\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=... \\ $$

Question Number 160922 Answers: 1 Comments: 0

monter que (3+(√5))^n +(3−(√5))^(n ) est divisible par 2^n beson d′aide svp

$${monter}\:{que}\:\left(\mathrm{3}+\sqrt{\mathrm{5}}\right)^{{n}} +\left(\mathrm{3}−\sqrt{\mathrm{5}}\right)^{{n}\:} \\ $$$${est}\:{divisible}\:{par}\:\mathrm{2}^{{n}} \\ $$$${beson}\:{d}'{aide}\:{svp} \\ $$

Question Number 160921 Answers: 0 Comments: 0

Find: 𝛀 =∫_( 1) ^( 21) (dx/e^([2x + (1/4)]) ) ; [∗]-GIF

$$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{1}} {\overset{\:\mathrm{21}} {\int}}\:\frac{\mathrm{dx}}{\boldsymbol{\mathrm{e}}^{\left[\mathrm{2}\boldsymbol{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\right]} }\:\:\:;\:\:\:\left[\ast\right]-\mathrm{GIF} \\ $$

Question Number 160917 Answers: 1 Comments: 0

Calculate a)lim_(x→+∞) (((x−1)/(x+1)))^x^2 b) lim_(x→0) ((2^(1/x) −1)/(2^(1/x) +1))

$${Calculate} \\ $$$$\left.{a}\right)\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\right)^{{x}^{\mathrm{2}} } \\ $$$$\left.{b}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}^{\frac{\mathrm{1}}{{x}}} −\mathrm{1}}{\mathrm{2}^{\frac{\mathrm{1}}{{x}}} +\mathrm{1}} \\ $$

Question Number 160912 Answers: 1 Comments: 0

lim_(x→0) ((tan (x+2)tan (2−x)−tan^2 (2))/(3x tan x)) =?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\mathrm{x}+\mathrm{2}\right)\mathrm{tan}\:\left(\mathrm{2}−\mathrm{x}\right)−\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{2}\right)}{\mathrm{3x}\:\mathrm{tan}\:\mathrm{x}}\:=? \\ $$

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