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Question Number 93827 Answers: 0 Comments: 1

simplify: (((cosα+isinα)^3 )/((sinβ+icosβ)^4 ))

$${simplify}:\:\frac{\left({cos}\alpha+\boldsymbol{\mathrm{i}}{sin}\alpha\right)^{\mathrm{3}} }{\left({sin}\beta+\boldsymbol{\mathrm{i}}{cos}\beta\right)^{\mathrm{4}} } \\ $$

Question Number 93824 Answers: 1 Comments: 0

Question Number 93820 Answers: 1 Comments: 1

∫ ((x^2 dx)/(√(x^2 −x+1)))

$$\int\:\frac{{x}^{\mathrm{2}} \:{dx}}{\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{1}}}\: \\ $$

Question Number 93818 Answers: 1 Comments: 0

(y−xy^2 )dx +(x+x^2 y^2 )dy = 0

$$\left(\mathrm{y}−\mathrm{xy}^{\mathrm{2}} \right)\mathrm{dx}\:+\left(\mathrm{x}+\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} \right)\mathrm{dy}\:=\:\mathrm{0} \\ $$

Question Number 93815 Answers: 1 Comments: 0

(D^2 +6D+9)y = (e^(−3x) /x^3 )

$$\left(\mathrm{D}^{\mathrm{2}} +\mathrm{6D}+\mathrm{9}\right)\mathrm{y}\:=\:\frac{\mathrm{e}^{−\mathrm{3x}} }{\mathrm{x}^{\mathrm{3}} }\: \\ $$

Question Number 93821 Answers: 1 Comments: 3

lim_(x→+∞) ln(e^x +1)−x =

$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\mathrm{ln}\left(\mathrm{e}^{{x}} +\mathrm{1}\right)−{x}\:=\: \\ $$

Question Number 93804 Answers: 1 Comments: 3

∫ x (((3x−1)/(x+2)))^(1/(3 )) dx ?

$$\int\:{x}\:\sqrt[{\mathrm{3}\:\:}]{\frac{\mathrm{3}{x}−\mathrm{1}}{{x}+\mathrm{2}}}\:{dx}\:?\: \\ $$

Question Number 93791 Answers: 0 Comments: 1

Question Number 94574 Answers: 1 Comments: 1

∫((√(cosx))/((√(sinx )) +(√(cosx))))dx=?

$$\int\frac{\sqrt{\mathrm{cosx}}}{\sqrt{\mathrm{sinx}\:}\:+\sqrt{\mathrm{cosx}}}\mathrm{dx}=? \\ $$

Question Number 93787 Answers: 0 Comments: 4

Question Number 93786 Answers: 3 Comments: 0

find f(x) such that f ′(x)=f^(−1) (x)

$${find}\:{f}\left({x}\right)\:{such}\:{that} \\ $$$${f}\:'\left({x}\right)={f}^{−\mathrm{1}} \left({x}\right) \\ $$

Question Number 93782 Answers: 0 Comments: 0

find (a/b) a=Σ_(k=1) ^∞ (1/(√(2k))) b=Σ_(k=0) ^∞ (1/(√(2k+1)))

$${find}\:\frac{{a}}{{b}} \\ $$$${a}=\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\sqrt{\mathrm{2}{k}}} \\ $$$${b}=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\sqrt{\mathrm{2}{k}+\mathrm{1}}} \\ $$$$ \\ $$

Question Number 93764 Answers: 0 Comments: 3

define Σ_(x=0) ^k ((n!)/(x!(n−x)!)) without Σ symbol

$$\mathrm{define} \\ $$$$\underset{{x}=\mathrm{0}} {\overset{{k}} {\sum}}\frac{{n}!}{{x}!\left({n}−{x}\right)!} \\ $$$$\mathrm{without}\:\Sigma\:\mathrm{symbol} \\ $$

Question Number 93762 Answers: 1 Comments: 0

Question Number 93742 Answers: 0 Comments: 5

No my post option again?? at Tinkutara. because i cannot find my post options again

$$\mathrm{No}\:\mathrm{my}\:\mathrm{post}\:\mathrm{option}\:\mathrm{again}?? \\ $$$$\mathrm{at}\:\mathrm{Tinkutara}. \\ $$$$\mathrm{because}\:\mathrm{i}\:\mathrm{cannot}\:\mathrm{find}\:\mathrm{my}\:\mathrm{post}\:\mathrm{options}\:\mathrm{again} \\ $$

Question Number 93732 Answers: 0 Comments: 1

Find the n-th derivative of f(x)=sin(x)lnx

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{n}-\mathrm{th}\:\mathrm{derivative}\:\mathrm{of} \\ $$$$\mathrm{f}\left({x}\right)=\mathrm{sin}\left({x}\right){l}\mathrm{n}{x} \\ $$

Question Number 93733 Answers: 4 Comments: 10

Question Number 93730 Answers: 0 Comments: 3

what are the reasons for not using x = ((2c)/(−b ±(√(b^2 −4ac)))) as the quadratic formula? i proved it.

$$\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{reasons}\:\mathrm{for}\:\mathrm{not}\:\mathrm{using}\: \\ $$$$\:{x}\:=\:\frac{\mathrm{2}{c}}{−{b}\:\pm\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}\:\:\mathrm{as}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{formula}?\: \\ $$$$\mathrm{i}\:\mathrm{proved}\:\mathrm{it}. \\ $$

Question Number 93727 Answers: 0 Comments: 4

what is saw function?

$${what}\:{is}\:{saw}\:{function}? \\ $$

Question Number 93726 Answers: 0 Comments: 1

find the value in sexagesimal numeral system 3° × 15°=? 3 × 15°=?

$${find}\:{the}\:{value}\:{in}\:{sexagesimal}\:{numeral} \\ $$$${system} \\ $$$$\mathrm{3}°\:×\:\mathrm{15}°=? \\ $$$$\mathrm{3}\:×\:\mathrm{15}°=? \\ $$

Question Number 93725 Answers: 2 Comments: 0

Question Number 93724 Answers: 0 Comments: 0

∫_0 ^∞ ((x(√(e^x −1)))/(1−2cosh(x)))dx

$$\int_{\mathrm{0}} ^{\infty} \frac{{x}\sqrt{{e}^{{x}} −\mathrm{1}}}{\mathrm{1}−\mathrm{2}{cosh}\left({x}\right)}{dx} \\ $$

Question Number 93695 Answers: 2 Comments: 1

Question Number 93707 Answers: 0 Comments: 2

y y′′ = (y′)^2

$$\mathrm{y}\:\mathrm{y}''\:=\:\left(\mathrm{y}'\right)^{\mathrm{2}} \: \\ $$

Question Number 93691 Answers: 1 Comments: 3

If Σ_(i = 1) ^(10) (x_i +4) = 60 then find the value of x^ .

$$\boldsymbol{\mathrm{If}}\:\underset{\boldsymbol{{i}}\:=\:\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\left(\boldsymbol{\mathrm{x}}_{\mathrm{i}} +\mathrm{4}\right)\:=\:\mathrm{60}\:\:\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\bar {\boldsymbol{{x}}}. \\ $$

Question Number 93689 Answers: 0 Comments: 1

simply:(((cos2Θ−isin2Θ)^7 (cos3Θ+isin3Θ)^(−5) )/((cos4Θ+isin4Θ)^(12) (cos5Θ−isin5Θ)^(−6) ))

$${simply}:\frac{\left({cos}\mathrm{2}\Theta−\boldsymbol{{i}}{sin}\mathrm{2}\Theta\right)^{\mathrm{7}} \left({cos}\mathrm{3}\Theta+\boldsymbol{{i}}{sin}\mathrm{3}\Theta\right)^{−\mathrm{5}} }{\left({cos}\mathrm{4}\Theta+\boldsymbol{{i}}{sin}\mathrm{4}\Theta\right)^{\mathrm{12}} \left({cos}\mathrm{5}\Theta−\boldsymbol{{i}}{sin}\mathrm{5}\Theta\right)^{−\mathrm{6}} } \\ $$

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