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Question Number 168013 Answers: 2 Comments: 0

Question Number 168011 Answers: 2 Comments: 0

Solve (2x+5y+1)dx − (5x+2y−1)dy=0 Mastermind

$${Solve}\: \\ $$$$\left(\mathrm{2}{x}+\mathrm{5}{y}+\mathrm{1}\right){dx}\:−\:\left(\mathrm{5}{x}+\mathrm{2}{y}−\mathrm{1}\right){dy}=\mathrm{0} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168009 Answers: 1 Comments: 0

lim_(x→∞) (((√(4x^2 −4x+1))+3x)/( (√(x^2 +x−5))+x))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}+\mathrm{3}{x}}{\:\sqrt{{x}^{\mathrm{2}} +{x}−\mathrm{5}}+{x}}=? \\ $$

Question Number 168004 Answers: 1 Comments: 0

lim_(x→∞) (√(4x^2 −16x+1))−2x+3=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{16}{x}+\mathrm{1}}−\mathrm{2}{x}+\mathrm{3}=? \\ $$

Question Number 168000 Answers: 0 Comments: 0

Divide a^(5/2) −5a^2 b^(1/3) +10a^(3/2) b^(2/3) −10ab+5a^(1/2) b^(4/3) by a^(1/2) −b^(1/3)

$${Divide}\:{a}^{\frac{\mathrm{5}}{\mathrm{2}}} −\mathrm{5}{a}^{\mathrm{2}} {b}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{10}{a}^{\frac{\mathrm{3}}{\mathrm{2}}} {b}^{\frac{\mathrm{2}}{\mathrm{3}}} −\mathrm{10}{ab}+\mathrm{5}{a}^{\frac{\mathrm{1}}{\mathrm{2}}} {b}^{\frac{\mathrm{4}}{\mathrm{3}}} \:{by}\:{a}^{\frac{\mathrm{1}}{\mathrm{2}}} −{b}^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$

Question Number 167997 Answers: 0 Comments: 0

xy+3x+2y=−6 yx+y+3z=−3 zx+2z+x=2 find x and y and z

$${xy}+\mathrm{3}{x}+\mathrm{2}{y}=−\mathrm{6} \\ $$$${yx}+{y}+\mathrm{3}{z}=−\mathrm{3} \\ $$$${zx}+\mathrm{2}{z}+{x}=\mathrm{2} \\ $$$${find}\:{x}\:{and}\:{y}\:{and}\:{z} \\ $$$$ \\ $$

Question Number 167996 Answers: 0 Comments: 0

find dy/dx if y=((x+2)/( (√(x+1)))) by first principle

$${find}\:{dy}/{dx}\:{if}\:{y}=\frac{{x}+\mathrm{2}}{\:\sqrt{{x}+\mathrm{1}}}\:{by}\:{first}\:{principle} \\ $$

Question Number 167994 Answers: 0 Comments: 0

Question Number 167989 Answers: 2 Comments: 0

∫ ((3−cos x)/(3+cos x)) dx =?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\frac{\mathrm{3}−\mathrm{cos}\:{x}}{\mathrm{3}+\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$

Question Number 167986 Answers: 1 Comments: 0

cosxcos(π/6)−sin(π/6)sinx=(π/4)

$$\mathrm{cosxcos}\frac{\pi}{\mathrm{6}}−\mathrm{sin}\frac{\pi}{\mathrm{6}}\mathrm{sinx}=\frac{\pi}{\mathrm{4}} \\ $$

Question Number 167985 Answers: 2 Comments: 0

If af(x)+bf((1/x))=(1/x) where a≠b and x≠0 show that f(x)=((1/(a^2 −b^2 )))((a/x)−bx)

$$\mathrm{If}\:\:\mathrm{af}\left(\mathrm{x}\right)+\mathrm{bf}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)=\frac{\mathrm{1}}{\mathrm{x}}\:\mathrm{where}\: \\ $$$$\mathrm{a}\neq\mathrm{b}\:\mathrm{and}\:\:\mathrm{x}\neq\mathrm{0}\:\mathrm{show}\:\mathrm{that} \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\boldsymbol{\mathrm{b}}^{\mathrm{2}} }\right)\left(\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{x}}}−\boldsymbol{\mathrm{bx}}\right) \\ $$

Question Number 167983 Answers: 0 Comments: 0

lim_(x→2^x ) (((x+2)/(2−x)))=?

$$\underset{{x}\rightarrow\mathrm{2}^{{x}} } {\mathrm{lim}}\left(\frac{{x}+\mathrm{2}}{\mathrm{2}−{x}}\right)=? \\ $$

Question Number 167982 Answers: 0 Comments: 3

lim_(x→∞) (((√(4x^2 −4x+1))+3x)/( (√(x^2 +x−5))+x))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}+\mathrm{3}{x}}{\:\sqrt{{x}^{\mathrm{2}} +{x}−\mathrm{5}}+{x}}=? \\ $$

Question Number 167981 Answers: 1 Comments: 0

lim_(x→0) ((4^x −2^x )/(8^x −4^x ))=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{4}^{{x}} −\mathrm{2}^{{x}} }{\mathrm{8}^{{x}} −\mathrm{4}^{{x}} }=? \\ $$

Question Number 167980 Answers: 1 Comments: 3

lim_(x→∞) (√(4x^2 −16x+1))−2x+3=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{16}{x}+\mathrm{1}}−\mathrm{2}{x}+\mathrm{3}=? \\ $$

Question Number 167979 Answers: 1 Comments: 0

3 men and 4 women are to sit on a table. Calculate the number of possible sitting arrangements if (a) they sit in a row such that the men must not sit next to each other. (b) they sit in circular pattern and the clockwise and anticlockwise orders are considered the same.

$$\mathrm{3}\:\mathrm{men}\:\mathrm{and}\:\mathrm{4}\:\mathrm{women}\:\mathrm{are}\:\mathrm{to}\:\mathrm{sit}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{table}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{possible}\:\mathrm{sitting}\:\mathrm{arrangements}\:\mathrm{if} \\ $$$$\:\left({a}\right)\:\mathrm{they}\:\mathrm{sit}\:\mathrm{in}\:\mathrm{a}\:\mathrm{row}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{men}\:\mathrm{must}\:\mathrm{not}\:\mathrm{sit}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{other}. \\ $$$$\:\left({b}\right)\:\mathrm{they}\:\mathrm{sit}\:\mathrm{in}\:\mathrm{circular}\:\mathrm{pattern}\:\mathrm{and} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{the}\:\mathrm{clockwise}\:\mathrm{and}\:\mathrm{anticlockwise} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{orders}\:\mathrm{are}\:\mathrm{considered}\:\mathrm{the}\:\mathrm{same}. \\ $$

Question Number 167978 Answers: 0 Comments: 0

(((3 2 )),((4 5)) ) [A] = determinant (((3 2)),((4 5)))

$$\begin{pmatrix}{\mathrm{3}\:\:\:\:\:\mathrm{2}\:}\\{\mathrm{4}\:\:\:\:\:\:\mathrm{5}}\end{pmatrix}\:\:\left[{A}\right]\:=\begin{vmatrix}{\mathrm{3}\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{4}\:\:\:\:\:\:\mathrm{5}}\end{vmatrix} \\ $$

Question Number 167977 Answers: 1 Comments: 0

Prove that I_n =(1/2^(n+1) )∫_π ^(4nπ) xcos (x/2)dx=((2−π)/2^(np) )

$${Prove}\:{that} \\ $$$${I}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}^{{n}+\mathrm{1}} }\int_{\pi} ^{\mathrm{4}{n}\pi} {x}\mathrm{cos}\:\frac{{x}}{\mathrm{2}}{dx}=\frac{\mathrm{2}−\pi}{\mathrm{2}^{{np}} } \\ $$

Question Number 167976 Answers: 0 Comments: 0

Question Number 167974 Answers: 1 Comments: 0

Question Number 167970 Answers: 0 Comments: 0

Calculate: lim_(n→∞) Σ_(k=1) ^n (k^2 /n^3 )∙(k)^(1/k) =?

$$\mathrm{Calculate}:\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{k}^{\mathrm{2}} }{\mathrm{n}^{\mathrm{3}} }\centerdot\sqrt[{\mathrm{k}}]{\mathrm{k}}=? \\ $$

Question Number 167966 Answers: 1 Comments: 0

Question Number 167965 Answers: 1 Comments: 0

Question Number 167964 Answers: 1 Comments: 1

Question Number 167963 Answers: 0 Comments: 0

show that_β_(1 =( nΣxy−ΣxΣy)/(nΣx^2 −(Σx)^2 )=Σxy/Σ(xy)^(2 ) where x=(x−x^− ) and y=(y−y^− ) )

$$\:{show}\:{that}_{\beta_{\mathrm{1}\:=\left(\:{n}\Sigma{xy}−\Sigma{x}\Sigma{y}\right)/\left({n}\Sigma{x}^{\mathrm{2}} −\left(\Sigma{x}\right)^{\mathrm{2}} \right)=\Sigma{xy}/\Sigma\left({xy}\right)^{\mathrm{2}\:} \:\:\:\:\:\:\:{where}\:{x}=\left({x}−\overset{−} {{x}}\right)\:{and}\:{y}=\left({y}−\overset{−} {{y}}\right)\:\:} } \: \\ $$$$ \\ $$

Question Number 167956 Answers: 0 Comments: 0

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