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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

Question Number 190166 Answers: 0 Comments: 0

Question Number 190165 Answers: 1 Comments: 0

S_n =1+(1/2^2 )+(1/3^2 )+...+(1/n^2 ) => lim_(n→∞) S_n =¿

$${S}_{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+...+\frac{\mathrm{1}}{{n}^{\mathrm{2}} } \\ $$$$=>\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}{S}_{{n}} =¿ \\ $$

Question Number 190162 Answers: 2 Comments: 0

Question Number 190151 Answers: 2 Comments: 4

I saw this in a book (without explanation). Please show how. It is given that tan 2θ=(B/(A−C)) (A,B,C ∈R) . Find cos 2θ.

$${I}\:{saw}\:{this}\:{in}\:{a}\:{book}\:\left({without}\:{explanation}\right).\:{Please}\:{show}\:{how}. \\ $$$${It}\:{is}\:{given}\:{that}\:\mathrm{tan}\:\mathrm{2}\theta=\frac{{B}}{{A}−{C}}\:\:\left({A},{B},{C}\:\in\mathbb{R}\right)\:.\:{Find}\:\mathrm{cos}\:\mathrm{2}\theta. \\ $$

Question Number 190140 Answers: 2 Comments: 1

Question Number 190138 Answers: 1 Comments: 0

Question Number 190137 Answers: 2 Comments: 0

{ ((fog^(−1) (x)=3x+2)),((gof(x)=2x−1)) :} find f(x)=? and fof(3)=?

$$\begin{cases}{\mathrm{fog}^{−\mathrm{1}} \left(\mathrm{x}\right)=\mathrm{3x}+\mathrm{2}}\\{\mathrm{gof}\left(\mathrm{x}\right)=\mathrm{2x}−\mathrm{1}}\end{cases} \\ $$$${find}\:\:\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)=?\:\:\:\mathrm{and}\:\:\:\:\mathrm{fof}\left(\mathrm{3}\right)=? \\ $$

Question Number 190134 Answers: 0 Comments: 0

Question Number 190131 Answers: 1 Comments: 0

if: x^2 +y^2 +z^2 + 14 = 2(x + 2y + 3z) find: T=((xyz)/(x^3 +y^3 +z^3 ))

$$\:\mathrm{if}:\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \:+\:\mathrm{14}\:=\:\mathrm{2}\left(\mathrm{x}\:+\:\mathrm{2y}\:+\:\mathrm{3z}\right) \\ $$$$\:\mathrm{find}:\:\:\mathrm{T}=\frac{\mathrm{xyz}}{\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +\mathrm{z}^{\mathrm{3}} }\: \\ $$

Question Number 190129 Answers: 1 Comments: 0

Question Number 190115 Answers: 1 Comments: 0

if: (a+b)(a+1) = b find: P = (√(a^3 +b^3 −3ab))

$$\mathrm{if}:\:\:\left(\mathrm{a}+\mathrm{b}\right)\left(\mathrm{a}+\mathrm{1}\right)\:=\:\mathrm{b} \\ $$$$\:\mathrm{find}:\:\:\mathrm{P}\:=\:\:\sqrt{\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} −\mathrm{3ab}} \\ $$

Question Number 190106 Answers: 0 Comments: 0

Question Number 190104 Answers: 1 Comments: 0

In AB^Δ C : II_( a) ^( 2) =^? 4R ( r_( a) − r ) I : incircle center I_( a) : excircle center corresponding A R: circumcircle radius r: incircle radius r_( a) : excircle radius corresponding A

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{In}\:\:\mathrm{A}\overset{\Delta} {\mathrm{B}C}\:\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{II}_{\:{a}} ^{\:\mathrm{2}} \:\overset{?} {=}\:\mathrm{4}{R}\:\left(\:{r}_{\:{a}} \:−\:{r}\:\right) \\ $$$$ \\ $$$$\:\:\:\:\mathrm{I}\::\:{incircle}\:\:{center} \\ $$$$\:\:\:\mathrm{I}_{\:{a}} \::\:{excircle}\:{center}\:{corresponding}\:{A} \\ $$$$\:\:\:{R}:\:{circumcircle}\:{radius} \\ $$$$\:\:\:\:\:{r}:\:{incircle}\:{radius} \\ $$$$\:\:\:\:\:{r}_{\:{a}} \::\:{excircle}\:{radius}\:{corresponding}\:{A} \\ $$

Question Number 190100 Answers: 1 Comments: 1

Question Number 190098 Answers: 0 Comments: 0

Question Number 190095 Answers: 1 Comments: 0

Question Number 190094 Answers: 2 Comments: 0

Question Number 190093 Answers: 2 Comments: 3

prove that : c= ( (√5) +2)^( (1/3)) − ((√5) −2)^( (1/3)) is a rational number.

$$ \\ $$$$\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$ \\ $$$${c}=\:\left(\:\sqrt{\mathrm{5}}\:+\mathrm{2}\right)^{\:\frac{\mathrm{1}}{\mathrm{3}}} \:−\:\left(\sqrt{\mathrm{5}}\:−\mathrm{2}\right)^{\:\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\mathrm{is}\:\:\:\mathrm{a}\:\:{rational}\:\:\mathrm{number}. \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 190091 Answers: 1 Comments: 0

1. Find sin52° + sin8° − cos22° 2. If a^2 + (1/a^2 ) = 6 find a^3 + (1/a^3 ) 3. Find ((tan32° + tan13°)/(1 − tan32° ∙ tan13°))

$$\mathrm{1}.\:\mathrm{Find}\:\:\:\mathrm{sin52}°\:+\:\mathrm{sin8}°\:−\:\mathrm{cos22}° \\ $$$$\mathrm{2}.\:\mathrm{If}\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2}} }\:=\:\mathrm{6}\:\:\:\mathrm{find}\:\:\:\mathrm{a}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{3}} } \\ $$$$\mathrm{3}.\:\mathrm{Find}\:\:\:\frac{\mathrm{tan32}°\:+\:\mathrm{tan13}°}{\mathrm{1}\:−\:\mathrm{tan32}°\:\centerdot\:\mathrm{tan13}°} \\ $$

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