Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 564

Question Number 161946    Answers: 2   Comments: 0

Question Number 161945    Answers: 1   Comments: 0

Prove that ∫_0 ^∞ (((xcos(x)βˆ’sin(x))^2 )/x^6 )dx =(𝛑/(15))

$$\:\:\boldsymbol{{P}\mathrm{rove}}\:\boldsymbol{\mathrm{that}}\:\int_{\mathrm{0}} ^{\infty} \frac{\left(\boldsymbol{{xcos}}\left(\boldsymbol{{x}}\right)βˆ’\boldsymbol{{sin}}\left(\boldsymbol{{x}}\right)\right)^{\mathrm{2}} }{\boldsymbol{{x}}^{\mathrm{6}} }\boldsymbol{{dx}}\:=\frac{\boldsymbol{\pi}}{\mathrm{15}} \\ $$

Question Number 161939    Answers: 0   Comments: 0

Ξ£_(n=1) ^(1010) tg^2 (((Ο€n)/(2022)))=?

$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\mathrm{1010}} {\sum}}\boldsymbol{\mathrm{tg}}^{\mathrm{2}} \left(\frac{\pi\boldsymbol{\mathrm{n}}}{\mathrm{2022}}\right)=? \\ $$

Question Number 161931    Answers: 0   Comments: 4

If (( 1βˆ’sin(x)βˆ’cos(x))/(1+sin(x)βˆ’cos(x))) = (1/4) then find the value of: tan(x) + (1/(cos(x))) =?

$$ \\ $$$$\:\:\:\:\:\:\mathrm{I}{f}\:\:\:\:\frac{\:\mathrm{1}βˆ’{sin}\left({x}\right)βˆ’{cos}\left({x}\right)}{\mathrm{1}+{sin}\left({x}\right)βˆ’{cos}\left({x}\right)}\:=\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:{then}\:\:{find}\:{the}\:{value}\:{of}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{tan}\left({x}\right)\:+\:\frac{\mathrm{1}}{{cos}\left({x}\right)}\:=? \\ $$$$\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 161930    Answers: 1   Comments: 0

{ ((a_0 =βˆ’2 )),((a_n =a_(nβˆ’1) +2n)) :} ; a_n =?

$$\begin{cases}{{a}_{\mathrm{0}} =βˆ’\mathrm{2}\:}\\{{a}_{{n}} ={a}_{{n}βˆ’\mathrm{1}} +\mathrm{2}{n}}\end{cases}\:\:\:\:\:;\:{a}_{{n}} =? \\ $$

Question Number 161926    Answers: 0   Comments: 0

Question Number 161919    Answers: 1   Comments: 0

∫_(βˆ’βˆž) ^( ∞) sin(x^2 +x+1)dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int_{βˆ’\infty} ^{\:\infty} \:\mathrm{sin}\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right){dx}\: \\ $$$$\: \\ $$

Question Number 161917    Answers: 0   Comments: 0

∫_(βˆ’βˆž) ^( ∞) (1/( (√(x^4 +x+1)) )) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{βˆ’\infty} ^{\:\infty} \:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{4}} +{x}+\mathrm{1}}\:}\:{dx} \\ $$$$\: \\ $$

Question Number 161914    Answers: 1   Comments: 0

If , x^( 2) + 9y^( 2) + 4x +18y βˆ’23=0 then find the value of , M_ ax ( 3x+2y ) . βˆ’βˆ’βˆ’βˆ’βˆ’βˆ’βˆ’βˆ’βˆ’

$$\:\mathrm{If}\:, \\ $$$$\:\:\:{x}^{\:\mathrm{2}} \:+\:\mathrm{9}{y}^{\:\mathrm{2}} \:+\:\mathrm{4}{x}\:+\mathrm{18}{y}\:βˆ’\mathrm{23}=\mathrm{0} \\ $$$$ \\ $$$$\:{then}\:\:{find}\:{the}\:{value}\:\:{of}\:\:,\:\:\mathrm{M}_{\:} {ax}\:\left(\:\mathrm{3}{x}+\mathrm{2}{y}\:\right)\:. \\ $$$$\:βˆ’βˆ’βˆ’βˆ’βˆ’βˆ’βˆ’βˆ’βˆ’ \\ $$$$ \\ $$

Question Number 161912    Answers: 1   Comments: 6

Question Number 162027    Answers: 1   Comments: 0

Question Number 161907    Answers: 0   Comments: 1

(1)((1/2)+cos (Ο€/(20)))((1/2)+cos ((3Ο€)/(20)))((1/2)+cos ((9Ο€)/(20)))((1/2)+cos ((27Ο€)/(20)))=? (2) tan (Ο€/(30)) tan ((7Ο€)/(30)) tan ((11Ο€)/(30)) =?

$$\left(\mathrm{1}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{cos}\:\frac{\pi}{\mathrm{20}}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{20}}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{cos}\:\frac{\mathrm{9}\pi}{\mathrm{20}}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{cos}\:\frac{\mathrm{27}\pi}{\mathrm{20}}\right)=? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{tan}\:\frac{\pi}{\mathrm{30}}\:\mathrm{tan}\:\frac{\mathrm{7}\pi}{\mathrm{30}}\:\mathrm{tan}\:\frac{\mathrm{11}\pi}{\mathrm{30}}\:=? \\ $$

Question Number 161903    Answers: 2   Comments: 1

((1βˆ’sin(x)βˆ’cos(x))/(1+sin(x)βˆ’cos(x)))=???

$$\frac{\mathrm{1}βˆ’\boldsymbol{{sin}}\left(\boldsymbol{{x}}\right)βˆ’\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)}{\mathrm{1}+\boldsymbol{{sin}}\left(\boldsymbol{{x}}\right)βˆ’\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)}=??? \\ $$$$ \\ $$

Question Number 161900    Answers: 1   Comments: 0

0<x;y;z<1 (1-x)(1-y)(1-z)=xyz Find: Ξ© = min (((1-x)/(xy)) + ((1-y)/(yz)) + ((1-z)/(zx)))

$$\mathrm{0}<\mathrm{x};\mathrm{y};\mathrm{z}<\mathrm{1} \\ $$$$\left(\mathrm{1}-\mathrm{x}\right)\left(\mathrm{1}-\mathrm{y}\right)\left(\mathrm{1}-\mathrm{z}\right)=\mathrm{xyz} \\ $$$$\mathrm{Find}: \\ $$$$\Omega\:=\:\mathrm{min}\:\left(\frac{\mathrm{1}-\mathrm{x}}{\mathrm{xy}}\:+\:\frac{\mathrm{1}-\mathrm{y}}{\mathrm{yz}}\:+\:\frac{\mathrm{1}-\mathrm{z}}{\mathrm{zx}}\right) \\ $$

Question Number 161899    Answers: 2   Comments: 0

Find: 𝛀 =∫_( -∞) ^( ∞) (1/((1 + x^(2n) )^2 )) dx ; n∈Z

$$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:=\underset{\:-\infty} {\overset{\:\infty} {\int}}\frac{\mathrm{1}}{\left(\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \right)^{\mathrm{2}} }\:\mathrm{dx}\:\:;\:\:\mathrm{n}\in\mathbb{Z} \\ $$

Question Number 161884    Answers: 0   Comments: 2

Solve for real numbers: ((2^x + 2^(-1) ))^(1/7) = 1 + ((2^x - 2^(-1) ))^(1/7)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\sqrt[{\mathrm{7}}]{\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{2}^{-\mathrm{1}} }\:=\:\mathrm{1}\:+\:\sqrt[{\mathrm{7}}]{\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:-\:\mathrm{2}^{-\mathrm{1}} } \\ $$

Question Number 162231    Answers: 1   Comments: 0

nature et calcul ∫_0 ^1 ((lnx)/( (√(1βˆ’x))))dx

$${nature}\:{et}\:{calcul} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{lnx}}{\:\sqrt{\mathrm{1}βˆ’{x}}}{dx} \\ $$

Question Number 161875    Answers: 0   Comments: 0

Question Number 161888    Answers: 1   Comments: 5

help me ! solve this one : C_(40) ^(2n) = C_(40) ^(16+n)

$$\mathrm{help}\:\mathrm{me}\:! \\ $$$$\mathrm{solve}\:\mathrm{this}\:\mathrm{one}\::\:\mathrm{C}_{\mathrm{40}} ^{\mathrm{2n}} \:=\:\mathrm{C}_{\mathrm{40}} ^{\mathrm{16}+\mathrm{n}} \\ $$

Question Number 161868    Answers: 1   Comments: 0

((√(2+(√3))) )^x + (1/(((√(2+(√3))))^x )) = 2^x x=?

$$\:\:\left(\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\:\right)^{{x}} \:+\:\frac{\mathrm{1}}{\left(\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\right)^{{x}} }\:=\:\mathrm{2}^{{x}} \\ $$$$\:\:{x}=? \\ $$

Question Number 161867    Answers: 1   Comments: 0

lim_(xβ†’βˆž) ((√(x^2 +8x+9)) βˆ’(√(x^2 +5x+4)) )^(4x) = ?

$$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{8}{x}+\mathrm{9}}\:βˆ’\sqrt{{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{4}}\:\right)^{\mathrm{4}{x}} \:=\:? \\ $$

Question Number 161866    Answers: 1   Comments: 3

Question Number 161862    Answers: 0   Comments: 0

Question Number 161861    Answers: 1   Comments: 8

Prove that ((1^2 βˆ™2!+2^2 βˆ™3!+3^2 βˆ™4!+βˆ™βˆ™βˆ™+n^2 (n+1)!βˆ’2)/((n+1)!)) =n^2 +nβˆ’2

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\frac{\mathrm{1}^{\mathrm{2}} \centerdot\mathrm{2}!+\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{3}!+\mathrm{3}^{\mathrm{2}} \centerdot\mathrm{4}!+\centerdot\centerdot\centerdot+{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)!βˆ’\mathrm{2}}{\left({n}+\mathrm{1}\right)!} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:={n}^{\mathrm{2}} +{n}βˆ’\mathrm{2} \\ $$

Question Number 161860    Answers: 1   Comments: 0

Simplify ((1^2 βˆ™2!+2^2 βˆ™3!+3^2 βˆ™4!+βˆ™βˆ™βˆ™+n^2 (n+1)!βˆ’2)/((n+1)!)) to n^2 +nβˆ’2

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Simplify} \\ $$$$\frac{\mathrm{1}^{\mathrm{2}} \centerdot\mathrm{2}!+\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{3}!+\mathrm{3}^{\mathrm{2}} \centerdot\mathrm{4}!+\centerdot\centerdot\centerdot+{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)!βˆ’\mathrm{2}}{\left({n}+\mathrm{1}\right)!} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{to} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{n}^{\mathrm{2}} +\mathrm{n}βˆ’\mathrm{2} \\ $$

Question Number 161854    Answers: 1   Comments: 1

  Pg 559      Pg 560      Pg 561      Pg 562      Pg 563      Pg 564      Pg 565      Pg 566      Pg 567      Pg 568   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com