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AllQuestion and Answers: Page 113

Question Number 205770 Answers: 0 Comments: 0

If x,y,z>0 and xyz = 1 Prove that: ((((√2)x)^2 )/((1+xz)(1+xy))) + ((((√2)y)^2 )/((1+yz)(1+xy))) + ((((√2)z)^2 )/((1+xz)(1+yz))) ≥ (3/2)

$If x, y, z > 0 and xyz = 1$ $Prove that :$ $\frac{{(\sqrt{2} x)}^{2}}{(1 + xz) (1 + xy)} + \frac{{(\sqrt{2} y)}^{2}}{(1 + yz) (1 + xy)} + \frac{{(\sqrt{2} z)}^{2}}{(1 + xz) (1 + yz)} ⩾ \frac{3}{2}$

Question Number 205767 Answers: 1 Comments: 0

a,b,c ∈ℜ^+ a+b+c=1 a^2 /(1+b+c) + b^2 /(1+a+c) + c^2 /(1+a+b)≥k find k max. hint : inequality cauchy schwarz

$a, b, c \in ℜ^{+}$ $a + b + c = 1$ $a^{2} / (1 + b + c) + b^{2} / (1 + a + c) + c^{2} / (1 + a + b) ⩾ k$ $f i n d k m a x .$ $h i n t : i n e q u a l i t y c a u c h y s c h w a r z$

Question Number 205750 Answers: 2 Comments: 3

∫_0 ^(+∞) (1/(1+e^(2x) ))dx=?

$\int_{0}^{+ \infty} \frac{1}{1 + e^{2 x}} d x = ?$

Question Number 205749 Answers: 0 Comments: 0

whats the suficient condition to became the question σ^2 (1−a_i )[λ_i (1+a_i )−(1−a_i )(1−d_i )+(λ_i +k)] < 0

$w h a t s t h e s u f i c i e n t c o n d i t i o n t o b e c a m e t h e q u e s t i o n$ $σ^{2} (1 - a_{i}) [λ_{i} (1 + a_{i}) - (1 - a_{i}) (1 - d_{i}) + (λ_{i} + k)] < 0$

Question Number 205746 Answers: 1 Comments: 0

Question Number 205734 Answers: 5 Comments: 0

Question Number 205733 Answers: 1 Comments: 0

If a,b,c∈R^+ and a+b+c=6 Prove that: ((a^2 −4)/(4a^2 −9a + 6)) + ((b^2 −4)/(4b^2 −9b + 6)) + ((c^2 −4)/(4c^2 −9c + 6)) ≤ 0

$If a, b, c \in R^{+} and a + b + c = 6$ $Prove that :$ $\frac{a^{2} - 4}{{4 a}^{2} - 9 a + 6} + \frac{b^{2} - 4}{{4 b}^{2} - 9 b + 6} + \frac{c^{2} - 4}{{4 c}^{2} - 9 c + 6} ⩽ 0$

Question Number 205727 Answers: 1 Comments: 4

calculate lim_(x→0) ((e^x −cosx)/x^2 )

$c a l c u l a t e {l i m}_{x \to 0} \frac{e^{x} - c o s x}{x^{2}}$

Question Number 205716 Answers: 2 Comments: 0

lim_(n→∞) (((2n+1)(2n+3)...(4n+1))/((2n)(2n+2)...(4n))) = ?

$\lim_{n \to \infty} \frac{(2 n + 1) (2 n + 3) . . . (4 n + 1)}{(2 n) (2 n + 2) . . . (4 n)} = ?$

Question Number 205726 Answers: 1 Comments: 0

101 is chosen arbitrarily from the numbers 1,2,3,...,199,200. Prove that two of these selected numbers can be found such that one is divisible by the other.

Question Number 205685 Answers: 2 Comments: 0

Question Number 205683 Answers: 1 Comments: 0

Question Number 205682 Answers: 1 Comments: 2

Question Number 205681 Answers: 2 Comments: 0

Question Number 205680 Answers: 1 Comments: 0

solve ⌊x ⌋ + ⌊ x^2 ⌋ = ⌊ x^3 ⌋

$s o l v e$ $⌊ x ⌋ + ⌊ x^{2} ⌋ = ⌊ x^{3} ⌋$

Question Number 205690 Answers: 0 Comments: 3

Question Number 205673 Answers: 0 Comments: 0

Question Number 205672 Answers: 1 Comments: 0

Question Number 205671 Answers: 1 Comments: 0

Question Number 205670 Answers: 1 Comments: 0

Question Number 205669 Answers: 1 Comments: 0

Question Number 205660 Answers: 1 Comments: 0

Question Number 205657 Answers: 1 Comments: 0

Question Number 205656 Answers: 2 Comments: 0

Question Number 205725 Answers: 1 Comments: 0

Question Number 205645 Answers: 1 Comments: 0

Find: Ω = ∫_0 ^( (𝛑/2)) ((sin^2 x)/(2 cosx + 3 sinx)) dx = ?

$Find : Ω = \int_{0}^{\frac{π}{2}} \frac{\sin^{2} x}{2 cosx + 3 sinx} dx = ?$

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