Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 482

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)) =?

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

Question Number 160910    Answers: 1   Comments: 0

Question Number 160909    Answers: 2   Comments: 0

How many 3−digits number such that sum of its digits is 11 ?

$${How}\:\:{many}\:\:\mathrm{3}−{digits}\:\:{number}\:\:{such}\:\:{that}\:\:{sum}\:\:{of}\:\:{its}\:\:{digits}\:\:{is}\:\:\mathrm{11}\:? \\ $$

Question Number 160908    Answers: 0   Comments: 1

x,y,z ∈ R^+ Find the minimum value of this expression ((xyz)/((1+3x)(x+8y)(y+9z)(6+z)))

$${x},{y},{z}\:\:\in\:\:\mathbb{R}^{+} \\ $$$${Find}\:\:{the}\:\:{minimum}\:\:{value}\:\:{of}\:\:{this}\:\:{expression}\: \\ $$$$\:\:\:\:\:\:\frac{{xyz}}{\left(\mathrm{1}+\mathrm{3}{x}\right)\left({x}+\mathrm{8}{y}\right)\left({y}+\mathrm{9}{z}\right)\left(\mathrm{6}+{z}\right)}\:\: \\ $$$$ \\ $$

Question Number 160906    Answers: 0   Comments: 0

Question Number 160903    Answers: 2   Comments: 0

(1+x^2 )y ′= 2xy +(1+x^2 )^2

$$\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}\:'=\:\mathrm{2}{xy}\:+\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} \: \\ $$

Question Number 160902    Answers: 1   Comments: 0

∫ (dx/( (√(sin^3 x)) (√(cos^5 x)))) =?

$$\:\:\int\:\frac{{dx}}{\:\sqrt{\mathrm{sin}\:^{\mathrm{3}} {x}}\:\sqrt{\mathrm{cos}\:^{\mathrm{5}} {x}}}\:=? \\ $$

Question Number 160900    Answers: 0   Comments: 2

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

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

Question Number 160895    Answers: 1   Comments: 0

Prove that: ∫_( 0) ^( 1) ((ln(x))/(x^n + x^(n-1) + ... + 1)) dx = (1/n^2 ) [𝛙^((1)) ((2/n)) - 𝛙^((1)) ((1/n))]

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{x}^{\boldsymbol{\mathrm{n}}-\mathrm{1}} \:+\:...\:+\:\mathrm{1}}\:\mathrm{dx}\:=\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} }\:\left[\boldsymbol{\psi}^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{2}}{\mathrm{n}}\right)\:-\:\boldsymbol{\psi}^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{1}}{\mathrm{n}}\right)\right] \\ $$

Question Number 160894    Answers: 1   Comments: 0

  Pg 477      Pg 478      Pg 479      Pg 480      Pg 481      Pg 482      Pg 483      Pg 484      Pg 485      Pg 486   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com