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Question Number 147788 Answers: 0 Comments: 0

Question Number 147784 Answers: 2 Comments: 0

Question Number 147778 Answers: 3 Comments: 0

Question Number 147761 Answers: 0 Comments: 0

Question Number 147809 Answers: 1 Comments: 0

((sin^6 (𝛂) + cos^6 (𝛂) - 1)/(sin^4 (𝛂) - sin^2 (𝛂))) = ?

$$\frac{\boldsymbol{{sin}}^{\mathrm{6}} \left(\boldsymbol{\alpha}\right)\:+\:\boldsymbol{{cos}}^{\mathrm{6}} \left(\boldsymbol{\alpha}\right)\:-\:\mathrm{1}}{\boldsymbol{{sin}}^{\mathrm{4}} \left(\boldsymbol{\alpha}\right)\:-\:\boldsymbol{{sin}}^{\mathrm{2}} \left(\boldsymbol{\alpha}\right)}\:=\:? \\ $$

Question Number 147753 Answers: 1 Comments: 0

Find a point on the curve y=x^2 −2x−3 at which the tangent is parallel to the x-axis

$${Find}\:{a}\:{point}\:{on}\:{the}\:{curve} \\ $$$$\:{y}={x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{3}\:{at}\:{which}\:{the}\:{tangent}\:{is} \\ $$$$\:{parallel}\:{to}\:{the}\:{x}-{axis} \\ $$

Question Number 147756 Answers: 0 Comments: 0

Question Number 147749 Answers: 1 Comments: 0

∫(((√(2−x^2 ))+(√(2+x^2 )))/( (√(4−x^4 ))))dx

$$\int\frac{\sqrt{\mathrm{2}−{x}^{\mathrm{2}} }+\sqrt{\mathrm{2}+{x}^{\mathrm{2}} }}{\:\sqrt{\mathrm{4}−{x}^{\mathrm{4}} }}{dx} \\ $$

Question Number 147748 Answers: 1 Comments: 1

prove that curves x^(2 ) −y^2 =3 and xy=2 intersect at the right angle

$${prove}\:{that}\:{curves}\:{x}^{\mathrm{2}\:} −{y}^{\mathrm{2}} =\mathrm{3}\:{and} \\ $$$$\:{xy}=\mathrm{2}\:{intersect}\:{at}\:{the}\:{right}\:{angle}\: \\ $$$$ \\ $$

Question Number 147747 Answers: 0 Comments: 0

Question Number 147746 Answers: 1 Comments: 0

Question Number 147738 Answers: 2 Comments: 0

lim_(x→0) ((arctan x−arcsin x)/(sin^3 x)) =?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{arctan}\:{x}−\mathrm{arcsin}\:{x}}{\mathrm{sin}\:^{\mathrm{3}} {x}}\:=? \\ $$

Question Number 147737 Answers: 1 Comments: 0

Σ_(n≥1) (1/n^2 )(1+(1/2)+(1/3)+...+(1/n))^2 =?

$$\:\underset{{n}\geqslant\mathrm{1}} {\sum}\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+...+\frac{\mathrm{1}}{{n}}\right)^{\mathrm{2}} =? \\ $$

Question Number 147714 Answers: 1 Comments: 0

Resoudre log_a (x^2 ) > log_a^2 (3x−2) avec a∈R_+ \{1} NB: a et a^2 sont les bases des logarithmes des nombres de l′ine^ galite.. les resultats se donnerons soua forme d′ine^ galite selon les cas..

$$\mathrm{Resoudre} \\ $$$$\mathrm{log}_{\mathrm{a}} \left(\mathrm{x}^{\mathrm{2}} \right)\:>\:\mathrm{log}_{\mathrm{a}^{\mathrm{2}} } \left(\mathrm{3x}−\mathrm{2}\right) \\ $$$$\mathrm{avec}\:\:\mathrm{a}\in\mathbb{R}_{+} \backslash\left\{\mathrm{1}\right\} \\ $$$$\mathrm{NB}:\:\mathrm{a}\:\mathrm{et}\:\mathrm{a}^{\mathrm{2}} \:\mathrm{sont}\:\mathrm{les}\:\mathrm{bases}\:\mathrm{des}\:\mathrm{logarithmes} \\ $$$$\mathrm{des}\:\mathrm{nombres}\:\mathrm{de}\:\mathrm{l}'\mathrm{in}\acute {\mathrm{e}galite}.. \\ $$$$\mathrm{les}\:\mathrm{resultats}\:\mathrm{se}\:\mathrm{donnerons}\:\mathrm{soua}\:\mathrm{forme} \\ $$$$\mathrm{d}'\mathrm{in}\acute {\mathrm{e}galite}\:\mathrm{selon}\:\mathrm{les}\:\mathrm{cas}.. \\ $$

Question Number 147713 Answers: 1 Comments: 0

Find a point on the curve y=(√x) where the tangent makes an angle 45° with the positive x-axis

$${Find}\:{a}\:{point}\:{on}\:{the}\:{curve}\:{y}=\sqrt{{x}} \\ $$$${where}\:{the}\:{tangent}\:{makes}\:{an}\:{angle}\: \\ $$$$\mathrm{45}°\:{with}\:{the}\:{positive}\:{x}-{axis} \\ $$

Question Number 147711 Answers: 1 Comments: 0

Determiner l′original de laplace F(x)=(1/((x^2 +x+1)^2 ))

$${Determiner}\:{l}'{original}\:{de}\:{laplace} \\ $$$${F}\left({x}\right)=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 147706 Answers: 1 Comments: 0

Question Number 147699 Answers: 1 Comments: 0

a^2 = 36^7 + 9^b + 6^8 ; a∈Z find b=?

$$\boldsymbol{{a}}^{\mathrm{2}} \:=\:\mathrm{36}^{\mathrm{7}} \:+\:\mathrm{9}^{\boldsymbol{{b}}} \:+\:\mathrm{6}^{\mathrm{8}} \:\:;\:\:\boldsymbol{{a}}\in\mathbb{Z} \\ $$$${find}\:\:\boldsymbol{{b}}=? \\ $$

Question Number 147689 Answers: 1 Comments: 0

(234)_5 ∙ (23)_5 = (x)_5 ⇒ x=?

$$\left(\mathrm{234}\right)_{\mathrm{5}} \:\centerdot\:\left(\mathrm{23}\right)_{\mathrm{5}} \:=\:\left({x}\right)_{\mathrm{5}} \:\:\Rightarrow\:\:\boldsymbol{{x}}=? \\ $$

Question Number 147688 Answers: 1 Comments: 0

find lim_(n→+∞) ∫_(1/n) ^(√n) xe^(−x^2 ) arctan(nx)dx

$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \int_{\frac{\mathrm{1}}{\mathrm{n}}} ^{\sqrt{\mathrm{n}}} \:\:\:\mathrm{xe}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{arctan}\left(\mathrm{nx}\right)\mathrm{dx} \\ $$

Question Number 147687 Answers: 2 Comments: 0

calculate lim_(n→0) ((e^(−nx^2 ) −nx−1)/x^3 )

$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow\mathrm{0}} \:\frac{\mathrm{e}^{−\mathrm{nx}^{\mathrm{2}} } −\mathrm{nx}−\mathrm{1}}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 147686 Answers: 0 Comments: 0

Question Number 147685 Answers: 2 Comments: 0

calculate lim_(x→0) ((sin(2sinx))/x^2 )

$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{sin}\left(\mathrm{2sinx}\right)}{\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 147684 Answers: 0 Comments: 0

decompse F(x)=(x^3 /((x^2 +1)^4 )) inside C(x)

$$\mathrm{decompse}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{x}^{\mathrm{3}} }{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{4}} }\:\:\:\mathrm{inside}\:\mathrm{C}\left(\mathrm{x}\right) \\ $$

Question Number 147683 Answers: 1 Comments: 0

let F(x)=(1/((x+1)^5 (2x−3)^4 )) 1) find ∫ F(x)dx 2)en deduire la decomposition de F en element simples

$$\mathrm{let}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{5}} \left(\mathrm{2x}−\mathrm{3}\right)^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right)\:\mathrm{find}\:\int\:\mathrm{F}\left(\mathrm{x}\right)\mathrm{dx} \\ $$$$\left.\mathrm{2}\right)\mathrm{en}\:\mathrm{deduire}\:\mathrm{la}\:\mathrm{decomposition}\:\mathrm{de}\:\mathrm{F}\:\mathrm{en}\:\mathrm{element}\:\mathrm{simples} \\ $$

Question Number 147682 Answers: 0 Comments: 0

decompose F(x)=(1/((x^n −1)(x^2 +x+1))) dans C(x) puis dans R(x)

$$\mathrm{decompose}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{n}} −\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)}\:\mathrm{dans}\:\mathrm{C}\left(\mathrm{x}\right)\:\mathrm{puis}\:\mathrm{dans}\:\mathrm{R}\left(\mathrm{x}\right) \\ $$

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