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AllQuestion and Answers: Page 584

Question Number 154542 Answers: 1 Comments: 0

Question Number 154530 Answers: 0 Comments: 0

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)

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

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

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

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

$if S_{n} (t) = n^{1 - t} (\frac{{(n + 1)}^{2 t}}{{(\sqrt[n + 1]{(n + 1)!})}^{t}} - \frac{n^{2 t}}{{(\sqrt[n]{n!})}^{t}})$ $with t > 0$ $Double subscripts: use braces to clarify$

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))

$If a; b; c > 0 and n \in N^{+} then :$ $\frac{a^{2 n} + b^{2 n} + c^{2 n}}{a^{n} b^{n} + b^{n} c^{n} + c^{n} a^{n}} ⩾ \frac{\sqrt{3 \cdot (a^{2} + b^{2} + c^{2})}}{a + b + c}$

Question Number 154478 Answers: 1 Comments: 0

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

$You can't use 'macro parameter character #' in math mode$ $\int_{0}^{\infty} \frac{{s i n}^{3} (x) . l n (x)}{x} d x \overset{?}{=} \frac{π}{8} (- 2 γ + l n (3)) . . . . . ◼ m . n$

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)=?

$s o i t : y^{″} - 3 y^{'} - 4 y = 3 e^{3 x} a v e c,$ $f (o) = - \frac{1}{2} e t f^{'} (0) = 4$ $a l o r s f (1) = ?$

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))))

$\underset{n = 1}{\prod^{\infty}} \frac{{(1 + \frac{1}{n})}^{\frac{1}{2}}}{1 + \frac{1}{2 n}}$

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 = ??

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

Question Number 154469 Answers: 1 Comments: 0

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

$p r o v e : \int_{0}^{1} l n (4 - 2 x + x^{2}) d x = 2 l n (\frac{2}{e}) + \frac{π}{\sqrt{3}}$

Question Number 154444 Answers: 2 Comments: 1

Question Number 154441 Answers: 1 Comments: 1

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

$\underset{n = 1}{\prod^{\infty}} \frac{{(1 + \frac{1}{n})}^{2}}{1 + \frac{2}{n}}$

Question Number 154440 Answers: 0 Comments: 0

arcsec(sec+2)=??

$a r c s e c (s e c + 2) = ? ?$

Question Number 154437 Answers: 3 Comments: 0

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

$\int_{0}^{\frac{π}{2}} a r c o s (\frac{c o s x}{1 + 2 c o s x}) d x$

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

$\int \frac{a^{2} \sin^{2} θ + b^{2} \cos^{2} θ}{a^{4} \sin^{2} θ + b^{4} \cos^{2} θ} d θ$

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