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Question Number 215114 Answers: 1 Comments: 0

Question Number 215107 Answers: 0 Comments: 4

Question Number 215094 Answers: 1 Comments: 11

Question Number 215092 Answers: 1 Comments: 2

Question Number 215091 Answers: 1 Comments: 0

Σ_(n=0) ^∞ (−1)^n (( Γ^( 2) (n+1))/(Γ (2n+1))) = ? −−− β (p ,q ) = (( Γ (p)Γ(q))/(Γ(p+q )))

$$ \\ $$$$\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \:\frac{\:\Gamma^{\:\mathrm{2}} \left({n}+\mathrm{1}\right)}{\Gamma\:\left(\mathrm{2}{n}+\mathrm{1}\right)}\:=\:? \\ $$$$\:\:\:\:\:\:−−− \\ $$$$\:\:\:\:\beta\:\left({p}\:,{q}\:\right)\:=\:\frac{\:\Gamma\:\left({p}\right)\Gamma\left({q}\right)}{\Gamma\left({p}+{q}\:\right)} \\ $$

Question Number 215089 Answers: 1 Comments: 0

log _2 x + log _3 (x+1) = 5 x = ?

$$\:\:\mathrm{log}\:_{\mathrm{2}} \:\mathrm{x}\:+\:\mathrm{log}\:_{\mathrm{3}} \:\left(\mathrm{x}+\mathrm{1}\right)\:=\:\mathrm{5}\: \\ $$$$\:\mathrm{x}\:=\:? \\ $$

Question Number 215809 Answers: 1 Comments: 0

If f(x) = 2 + ∫_1 ^(−x^3 ) (√(2+u^2 )) du find the value of (d/dx) [f^(−1) (x)]_(x=2)

$$\:\:\:\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{2}\:+\:\underset{\mathrm{1}} {\overset{−\mathrm{x}^{\mathrm{3}} } {\int}}\sqrt{\mathrm{2}+\mathrm{u}^{\mathrm{2}} }\:\mathrm{du}\: \\ $$$$\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{d}}{\mathrm{dx}}\:\left[\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)\right]_{\mathrm{x}=\mathrm{2}} \\ $$

Question Number 215808 Answers: 1 Comments: 0

⇃

$$\:\:\:\downharpoonleft\underline{\:} \\ $$

Question Number 215086 Answers: 0 Comments: 0

Question Number 215180 Answers: 1 Comments: 1

{ ((x^2 + y = 31)),((y^2 + x = 41)) :} ⇒ (x ; y) = ?

$$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{y}\:\:=\:\:\mathrm{31}}\\{\mathrm{y}^{\mathrm{2}} \:\:+\:\:\mathrm{x}\:\:=\:\:\mathrm{41}}\end{cases}\:\:\:\:\:\Rightarrow\:\:\:\left(\mathrm{x}\:;\:\mathrm{y}\right)\:=\:? \\ $$

Question Number 215072 Answers: 1 Comments: 4

x^2 + 2000x + 1 = 0 Roots: a and b x^2 − 2008x − 1 = 0 Roots: c and d Find: (a+c)(b+d)(a−d)(b−c) = ?

$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2000x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{Roots}:\:\:\boldsymbol{\mathrm{a}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{b}} \\ $$$$\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{2008x}\:−\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{Roots}:\:\:\boldsymbol{\mathrm{c}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{d}} \\ $$$$\mathrm{Find}:\:\:\left(\mathrm{a}+\mathrm{c}\right)\left(\mathrm{b}+\mathrm{d}\right)\left(\mathrm{a}−\mathrm{d}\right)\left(\mathrm{b}−\mathrm{c}\right)\:=\:? \\ $$

Question Number 215067 Answers: 0 Comments: 1

Question Number 215061 Answers: 1 Comments: 0

∫_0 ^( ∞) ∫_0 ^( ∞) e^( − (( x^2 +y^2 )/2)) sin(xy )dxdy=?

$$ \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \int_{\mathrm{0}} ^{\:\infty} \mathrm{e}^{\:\:−\:\frac{\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{\mathrm{2}}} \mathrm{sin}\left({xy}\:\right){dxdy}=? \\ $$$$ \\ $$

Question Number 215052 Answers: 2 Comments: 0

Question Number 215051 Answers: 1 Comments: 0

lim_(n→∞) Π_(k=1) ^n ((k^2 +1)/( (√(k^2 +4))))=?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\frac{{k}^{\mathrm{2}} +\mathrm{1}}{\:\sqrt{{k}^{\mathrm{2}} +\mathrm{4}}}=? \\ $$$$ \\ $$

Question Number 215048 Answers: 0 Comments: 2

Solve for a, b, c ∈ R (1/a) + (1/(b+c)) = (1/2) (1/b) + (1/(c+a)) = (1/3) (1/c) + (1/(a+b)) = (1/4)

$$\mathrm{Solve}\:\:\mathrm{for}\:\:{a},\:{b},\:{c}\:\in\:\mathbb{R} \\ $$$$\:\:\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}+{c}}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}+{a}}\:=\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\:\:\:\frac{\mathrm{1}}{{c}}\:+\:\frac{\mathrm{1}}{{a}+{b}}\:=\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 215041 Answers: 0 Comments: 0

3 numbers are selected randomly from 0 to 10 (Continuous). forming a new range. what is the probability that the new range is less than or equal to 2? new range = max-min

$$ \\ $$3 numbers are selected randomly from 0 to 10 (Continuous). forming a new range. what is the probability that the new range is less than or equal to 2? new range = max-min

Question Number 215232 Answers: 1 Comments: 0

Question Number 215231 Answers: 1 Comments: 0

Question Number 215230 Answers: 1 Comments: 0

Question Number 215229 Answers: 1 Comments: 0

Question Number 215032 Answers: 1 Comments: 1

Question Number 215020 Answers: 1 Comments: 2

f: [0 , 1] →R is given. f ′′ is continuous . by the way f(0)=f(1). prove that : determinant (((∫_0 ^( 1) ( f ′′ (x))^( 2) dx ≥ 3(f ′(1))^2 )))

$$ \\ $$$$\:\:\:\:{f}:\:\:\left[\mathrm{0}\:,\:\mathrm{1}\right]\:\rightarrow\mathbb{R}\:{is}\:{given}. \\ $$$$\:\:\:\:{f}\:''\:\:\:\:{is}\:{continuous}\:. \\ $$$$\:\:\:\:{by}\:{the}\:{way}\:\:{f}\left(\mathrm{0}\right)={f}\left(\mathrm{1}\right). \\ $$$$\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$\:\:\:\: \\ $$$$\begin{array}{|c|}{\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\:{f}\:''\:\left({x}\right)\right)^{\:\mathrm{2}} {dx}\:\geqslant\:\mathrm{3}\left({f}\:'\left(\mathrm{1}\right)\right)^{\mathrm{2}} }\\\hline\end{array} \\ $$$$ \\ $$

Question Number 215017 Answers: 2 Comments: 0

Re^ soudre dans C l′e^ quation : sin(z) = 2.

$${R}\acute {{e}soudre}\:{dans}\:\mathbb{C}\:{l}'\acute {{e}quation}\:: \\ $$$${sin}\left({z}\right)\:=\:\mathrm{2}. \\ $$

Question Number 215011 Answers: 0 Comments: 0

Question Number 215005 Answers: 1 Comments: 0

a,b,c,d∈R such that, (a+b)(c+d)=2 (a+c)(b+d)=3 (a+d)(b+c)=4 find: (a^2 +b^2 +c^2 +d^2 )_(minimum.)

$$\:{a},{b},{c},{d}\in{R}\:{such}\:{that}, \\ $$$$\:\left({a}+{b}\right)\left({c}+{d}\right)=\mathrm{2} \\ $$$$\:\left({a}+{c}\right)\left({b}+{d}\right)=\mathrm{3} \\ $$$$\:\left({a}+{d}\right)\left({b}+{c}\right)=\mathrm{4}\: \\ $$$$\:{find}:\:\:\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} \right)_{{minimum}.} \\ $$

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