Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 554

Question Number 154516 Answers: 0 Comments: 0

Question Number 154514 Answers: 0 Comments: 1

Question Number 154586 Answers: 1 Comments: 0

Question Number 154507 Answers: 2 Comments: 1

Question Number 154649 Answers: 0 Comments: 2

if n ∈ N^(>2) prove that [((n)^(1/3) + ((n + 2))^(1/3) )^3 ] + 1 = 0 (mod 8)

$$\mathrm{if}\:\:\mathrm{n}\:\in\:\mathbb{N}^{>\mathrm{2}} \:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\left[\left(\sqrt[{\mathrm{3}}]{\mathrm{n}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{n}\:+\:\mathrm{2}}\:\right)^{\mathrm{3}} \right]\:+\:\mathrm{1}\:=\:\mathrm{0}\:\left(\mathrm{mod}\:\mathrm{8}\right) \\ $$

Question Number 154620 Answers: 0 Comments: 0

Question Number 154497 Answers: 2 Comments: 0

Solve the equations: a) 2 (√(2x^3 - x)) = 3x^2 - 3x + 2 b) (√((x^4 + 16)/2)) + (√(2(x^2 + 4))) = 3x + 2

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equations}: \\ $$$$\left.\boldsymbol{\mathrm{a}}\right)\:\:\:\mathrm{2}\:\sqrt{\mathrm{2x}^{\mathrm{3}} \:-\:\mathrm{x}}\:=\:\mathrm{3x}^{\mathrm{2}} \:-\:\mathrm{3x}\:+\:\mathrm{2} \\ $$$$\left.\boldsymbol{\mathrm{b}}\right)\:\:\:\sqrt{\frac{\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{16}}{\mathrm{2}}}\:+\:\sqrt{\mathrm{2}\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4}\right)}\:=\:\mathrm{3x}\:+\:\mathrm{2} \\ $$

Question Number 154495 Answers: 1 Comments: 0

if S_n (t) = n^(1-t) ((((n+1)^(2t) )/(((((n+1)!))^(1/(n+1)) )^t )) - (n^(2t) /((((n!))^(1/n) )^t ))) with t>0 then lim_(n→∞) S_n (t) = te^t

Question Number 154493 Answers: 0 Comments: 0

If a;b;c>0 and n∈N^+ then: ((a^(2n) + b^(2n) + c^(2n) )/(a^n b^n + b^n c^n + c^n a^n )) ≥ ((√(3∙(a^2 + b^2 + c^2 )))/(a + b + c))

Question Number 154478 Answers: 1 Comments: 0

prove that # ∫_0 ^( ∞) (( sin^( 3) ( x ).ln( x ))/x) dx =^? (π/8) (−2γ +ln(3)) .....■ m.n

$$ \\ $$$$ \\ $$$$\:\:{prove}\:{that}\:# \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sin}^{\:\mathrm{3}} \left(\:{x}\:\right).{ln}\left(\:{x}\:\right)}{{x}}\:{dx}\:\overset{?} {=}\:\frac{\pi}{\mathrm{8}}\:\left(−\mathrm{2}\gamma\:+{ln}\left(\mathrm{3}\right)\right)\:.....\blacksquare\:{m}.{n}\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\: \\ $$$$ \\ $$

Question Number 154476 Answers: 3 Comments: 0

soit:y′′−3y′−4y=3e^(3x ) avec , f(o)=−(1/2) et f′(0)=4 alors f(1)=?

$${soit}:{y}''−\mathrm{3}{y}'−\mathrm{4}{y}=\mathrm{3}{e}^{\mathrm{3}{x}\:} \:{avec}\:, \\ $$$${f}\left({o}\right)=−\frac{\mathrm{1}}{\mathrm{2}}\:{et}\:{f}'\left(\mathrm{0}\right)=\mathrm{4} \\ $$$${alors}\:{f}\left(\mathrm{1}\right)=? \\ $$$$ \\ $$

Question Number 154475 Answers: 2 Comments: 4

Question Number 154467 Answers: 1 Comments: 0

Π_(n=1) ^∞ (((1+ (1/n))^(1/2) )/(1+ (1/(2n))))

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\left(\mathrm{1}+\:\frac{\mathrm{1}}{{n}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} }{\mathrm{1}+\:\frac{\mathrm{1}}{\mathrm{2}{n}}} \\ $$$$\: \\ $$

Question Number 154465 Answers: 0 Comments: 2

Question Number 154458 Answers: 1 Comments: 0

Question Number 154456 Answers: 1 Comments: 2

S=90^2 +91^2 +.....+100^2 = ??

$${S}=\mathrm{90}^{\mathrm{2}} +\mathrm{91}^{\mathrm{2}} +.....+\mathrm{100}^{\mathrm{2}} \:\:=\:\:?? \\ $$

Question Number 154469 Answers: 1 Comments: 0

prove:∫_0 ^( 1) ln (4− 2x +x^( 2) )dx =2ln((2/e)) +(π/( (√3)))

$$ \\ $$$${prove}:\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\:\left(\mathrm{4}−\:\mathrm{2}{x}\:+{x}^{\:\mathrm{2}} \right){dx}\:=\mathrm{2}{ln}\left(\frac{\mathrm{2}}{{e}}\right)\:+\frac{\pi}{\:\sqrt{\mathrm{3}}} \\ $$$$ \\ $$

Question Number 154444 Answers: 2 Comments: 1

Question Number 154441 Answers: 1 Comments: 1

Π_(n=1) ^∞ (( (1+ (1/n))^2 )/( 1+ (2/n) ))

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\:\left(\mathrm{1}+\:\frac{\mathrm{1}}{{n}}\right)^{\mathrm{2}} \:}{\:\mathrm{1}+\:\frac{\mathrm{2}}{{n}}\:} \\ $$$$\: \\ $$

Question Number 154440 Answers: 0 Comments: 0

arcsec(sec+2)=??

$${arcsec}\left({sec}+\mathrm{2}\right)=?? \\ $$

Question Number 154437 Answers: 3 Comments: 0

∫_0 ^(π/2) arcos(((cosx)/(1+2cosx)))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {arcos}\left(\frac{{cosx}}{\mathrm{1}+\mathrm{2}{cosx}}\right){dx} \\ $$

Question Number 154434 Answers: 1 Comments: 0

Question Number 154433 Answers: 0 Comments: 0

Question Number 154422 Answers: 0 Comments: 0

∫((a^2 sin^2 θ+b^2 cos^2 θ)/(a^4 sin^2 θ+b^4 cos^2 θ))dθ

$$\int\frac{\mathrm{a}^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \theta+\mathrm{b}^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} \theta}{\mathrm{a}^{\mathrm{4}} \mathrm{sin}\:^{\mathrm{2}} \theta+\mathrm{b}^{\mathrm{4}} \mathrm{cos}\:^{\mathrm{2}} \theta}\mathrm{d}\theta \\ $$

Question Number 154421 Answers: 2 Comments: 0

∫[((x/e))^x +((e/x))^x ]ln xdx

$$\int\left[\left(\frac{\mathrm{x}}{\mathrm{e}}\right)^{\mathrm{x}} +\left(\frac{\mathrm{e}}{\mathrm{x}}\right)^{\mathrm{x}} \right]\mathrm{ln}\:\mathrm{xdx} \\ $$

Question Number 154429 Answers: 0 Comments: 3

Pg 549 Pg 550 Pg 551 Pg 552 Pg 553 Pg 554 Pg 555 Pg 556 Pg 557 Pg 558

Contact: info@tinkutara.com