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Question Number 190241 Answers: 1 Comments: 0

show that a⊛b=a+ab+b is a monoid when G=Z

$${show}\:{that}\:{a}\circledast{b}={a}+{ab}+{b}\:{is}\:{a}\:{monoid}\:{when}\:{G}={Z} \\ $$

Question Number 190239 Answers: 0 Comments: 0

Question Number 190238 Answers: 0 Comments: 0

Question Number 190237 Answers: 0 Comments: 0

Question Number 190230 Answers: 2 Comments: 0

Question Number 190216 Answers: 2 Comments: 3

Question Number 190199 Answers: 1 Comments: 0

Question Number 190198 Answers: 1 Comments: 0

Question Number 190192 Answers: 3 Comments: 2

if a>b>0, find the minimum of a^2 +(1/((a−b)b))=?

$${if}\:{a}>{b}>\mathrm{0},\:{find}\:{the}\:{minimum}\:{of} \\ $$$${a}^{\mathrm{2}} +\frac{\mathrm{1}}{\left({a}−{b}\right){b}}=? \\ $$

Question Number 190191 Answers: 1 Comments: 0

Question Number 190186 Answers: 0 Comments: 1

determinant ((( If , Ω= ∫_0 ^( (π/2)) (( 4cos^( 2) (4x))/(3(1+sin^( 2) (2x ))))dx= a(√2) + b ))) ⇒ Find the value of , a− b=?

$$ \\ $$$$\:\:\:\:\begin{array}{|c|}{\:\:\:\:\:\:\:\:\:\mathrm{If}\:\:,\:\Omega=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\:\mathrm{4cos}^{\:\mathrm{2}} \:\left(\mathrm{4}{x}\right)}{\mathrm{3}\left(\mathrm{1}+\mathrm{sin}^{\:\mathrm{2}} \left(\mathrm{2}{x}\:\right)\right)}\mathrm{d}{x}=\:{a}\sqrt{\mathrm{2}}\:\:+\:{b}\:\:\:\:\:\:\:\:\:\:}\\\hline\end{array}\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:\mathrm{Find}\:\:\mathrm{the}\:\:\mathrm{value}\:\mathrm{of}\:\:\:,\:\:{a}−\:{b}=? \\ $$$$ \\ $$

Question Number 190185 Answers: 0 Comments: 1

In AB^Δ C : If , sin (A^ ) = (1/(2 (√( 2+ (√3))))) ⇒ A^ = ?

$$ \\ $$$$\:\:\:\:\:\:\mathrm{In}\:\mathrm{A}\overset{\Delta} {\mathrm{B}C}\:\::\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{If}\:,\:\mathrm{sin}\:\left(\hat {\mathrm{A}}\:\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}\:\sqrt{\:\mathrm{2}+\:\sqrt{\mathrm{3}}}}\:\:\:\:\:\Rightarrow\:\:\:\:\:\hat {\mathrm{A}}\:=\:?\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$

Question Number 190182 Answers: 0 Comments: 4

Lim_(x→π/2) ((sinx−sinx^(sinx) )/(1−sinx+logsinx)) a)4 b)2 c)1/2 d)none

$${Li}\underset{{x}\rightarrow\pi/\mathrm{2}} {{m}}\frac{{sinx}−{sinx}^{{sinx}} }{\mathrm{1}−{sinx}+{logsinx}} \\ $$$$\left.{a}\left.\right)\left.\mathrm{4}\left.\:\:\:\:\:\:\:\:{b}\right)\mathrm{2}\:\:\:\:\:\:\:\:\:\:{c}\right)\mathrm{1}/\mathrm{2}\:\:\:\:\:\:\:\:{d}\right){none} \\ $$

Question Number 190178 Answers: 0 Comments: 1

calculate lim_( n→∞) (( Γ ( (( n+3)/2) ))/(n^( (3/2)) .Γ ((n/2) ))) = ?

$$ \\ $$$$\:\:{calculate} \\ $$$$ \\ $$$$\:\:\:\:\mathrm{lim}_{\:\mathrm{n}\rightarrow\infty} \frac{\:\Gamma\:\left(\:\frac{\:{n}+\mathrm{3}}{\mathrm{2}}\:\right)}{{n}^{\:\frac{\mathrm{3}}{\mathrm{2}}} .\Gamma\:\left(\frac{{n}}{\mathrm{2}}\:\right)}\:=\:? \\ $$

Question Number 190172 Answers: 1 Comments: 0

Integrate ∫_0 ^1 Sin^2 (2Πx)dx

$${Integrate}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:{Sin}^{\mathrm{2}} \left(\mathrm{2}\Pi{x}\right){dx} \\ $$

Question Number 190169 Answers: 3 Comments: 3

Question Number 190168 Answers: 0 Comments: 2

1)∫^∞ _0 ((sin x)/(x^p +sin x))dx ,p>0 2)∫^∞ _π ((xcos x)/(x^p +x^q ))dx,p>0and q>0 3)∫^∞ _0 ((sin x^p )/( x^q ))dx, p>0,q>0 4)∫^2 _0 (dx/(∣ln x∣^p )) ,p>0 5)∫^1 _0 ((cos(1/(1−x)))/( ((1−x^2 ))^(1/n) ))dx 6)∫^∞ _0 (dx/(x^p ((sin^2 x))^(1/3) ))

$$\left.\mathrm{1}\right)\underset{\mathrm{0}} {\int}^{\infty} \frac{{sin}\:{x}}{{x}^{{p}} +{sin}\:{x}}{dx}\:,{p}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\underset{\pi} {\int}^{\infty} \frac{{xcos}\:{x}}{{x}^{{p}} +{x}^{{q}} }{dx},{p}>\mathrm{0}{and}\:{q}>\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\underset{\mathrm{0}} {\int}^{\infty} \frac{{sin}\:{x}^{{p}} }{\:{x}^{{q}} }{dx},\:{p}>\mathrm{0},{q}>\mathrm{0} \\ $$$$\left.\mathrm{4}\right)\underset{\mathrm{0}} {\int}^{\mathrm{2}} \frac{{dx}}{\mid{ln}\:{x}\mid^{{p}} }\:,{p}>\mathrm{0} \\ $$$$\left.\mathrm{5}\right)\underset{\mathrm{0}} {\int}^{\mathrm{1}} \frac{{cos}\frac{\mathrm{1}}{\mathrm{1}−{x}}}{\:\sqrt[{{n}}]{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$$$\left.\mathrm{6}\right)\underset{\mathrm{0}} {\int}^{\infty} \frac{{dx}}{{x}^{{p}} \sqrt[{\mathrm{3}}]{{sin}^{\mathrm{2}} {x}}} \\ $$

Question Number 190167 Answers: 0 Comments: 0