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Question Number 226745 Answers: 0 Comments: 1

if (x/(lm−n^2 ))=(y/(mn−l^2 ))=(z/(nl−m^2 )) then show lx+my+nz=0

$${if}\:\frac{{x}}{{lm}−{n}^{\mathrm{2}} }=\frac{{y}}{{mn}−{l}^{\mathrm{2}} }=\frac{{z}}{{nl}−{m}^{\mathrm{2}} } \\ $$$${then}\:{show}\:{lx}+{my}+{nz}=\mathrm{0} \\ $$$$ \\ $$

Question Number 226743 Answers: 0 Comments: 0

Prove:(1/(2ne))<(1/e)−(1−(1/n))^n <(1/(ne))

$$ \\ $$$${Prove}:\frac{\mathrm{1}}{\mathrm{2}{ne}}<\frac{\mathrm{1}}{{e}}−\left(\mathrm{1}−\frac{\mathrm{1}}{{n}}\right)^{{n}} <\frac{\mathrm{1}}{{ne}} \\ $$

Question Number 226738 Answers: 1 Comments: 0

Prove: lim_(v→∞) (√n)((1/2)+e^(−n) (Π_(k=1) ^(2n) (((2n)),(k) )^(1/(2n)) −Σ_(k=0) ^n (n^k /(k!))))=(1/( (√π)))((e/2)−((√2)/3))

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Prove}}: \\ $$$$\underset{{v}\rightarrow\infty} {\mathrm{lim}}\sqrt{{n}}\left(\frac{\mathrm{1}}{\mathrm{2}}+{e}^{−{n}} \left(\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}{n}} {\prod}}\begin{pmatrix}{\mathrm{2}{n}}\\{{k}}\end{pmatrix}^{\frac{\mathrm{1}}{\mathrm{2}{n}}} −\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{{n}^{{k}} }{{k}!}\right)\right)=\frac{\mathrm{1}}{\:\sqrt{\pi}}\left(\frac{{e}}{\mathrm{2}}−\frac{\sqrt{\mathrm{2}}}{\mathrm{3}}\right) \\ $$

Question Number 226736 Answers: 0 Comments: 4

Question Number 226732 Answers: 1 Comments: 0

Question Number 226728 Answers: 1 Comments: 0

Find: ∫_0 ^( (𝛑/4)) (dx/(1 + sin^2 x)) = ?

$$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{4}}} \:\frac{\mathrm{dx}}{\mathrm{1}\:+\:\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\:=\:? \\ $$

Question Number 226721 Answers: 4 Comments: 0

Question Number 226719 Answers: 0 Comments: 1

Question Number 226714 Answers: 0 Comments: 1

Question Number 226713 Answers: 0 Comments: 0

If p=(1/x)−(1/x^2 ) what should p=(((N)_4 )/((D)_4 )) (N)_4 means numerator of p in quaternary for x to be 777?

$$\:\:{If}\: \\ $$$${p}=\frac{\mathrm{1}}{{x}}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} } \\ $$$${what}\:{should}\:{p}=\frac{\left({N}\right)_{\mathrm{4}} }{\left({D}\right)_{\mathrm{4}} } \\ $$$$\left({N}\right)_{\mathrm{4}} \:{means}\:{numerator}\:{of}\:{p}\:\:{in} \\ $$$${quaternary}\:{for}\:{x}\:{to}\:{be}\:\mathrm{777}? \\ $$

Question Number 226705 Answers: 2 Comments: 0

Question Number 226702 Answers: 1 Comments: 0

∫((ln(x^2 +3x+2))/(x^2 +1))dx[

$$\int\frac{{ln}\left({x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{2}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}{dx}\left[\right. \\ $$

Question Number 226697 Answers: 1 Comments: 1

Question Number 226668 Answers: 1 Comments: 0

Question Number 226653 Answers: 0 Comments: 1

Σ_(k=1) ^∞ ((Si(πn))/n^2 )=?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{Si}\left(\pi{n}\right)}{{n}^{\mathrm{2}} }=? \\ $$

Question Number 226651 Answers: 3 Comments: 1

Question Number 226641 Answers: 3 Comments: 1

if log _8 a+log _4 b^2 =5 & log _8^b +log _4 a^2 =7 ab=?

$${if}\:\mathrm{log}\:_{\mathrm{8}} {a}+\mathrm{log}\:_{\mathrm{4}} {b}^{\mathrm{2}} =\mathrm{5} \\ $$$$\& \\ $$$$\mathrm{log}\:_{\mathrm{8}} ^{{b}} +\mathrm{log}\:_{\mathrm{4}} {a}^{\mathrm{2}} =\mathrm{7} \\ $$$${ab}=? \\ $$

Question Number 226675 Answers: 0 Comments: 5

Question Number 226638 Answers: 1 Comments: 1

Question Number 226635 Answers: 1 Comments: 0

Question Number 226622 Answers: 0 Comments: 2

Question Number 226626 Answers: 0 Comments: 0

Question Number 226624 Answers: 1 Comments: 1

Question Number 226619 Answers: 0 Comments: 3

factorise x^2 −qx−p^2 +5pq−6q^2

$${factorise} \\ $$$${x}^{\mathrm{2}} −{qx}−{p}^{\mathrm{2}} +\mathrm{5}{pq}−\mathrm{6}{q}^{\mathrm{2}} \\ $$

Question Number 226612 Answers: 0 Comments: 1

Question Number 226610 Answers: 2 Comments: 0

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