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Question Number 226785 Answers: 0 Comments: 4

Question Number 226780 Answers: 1 Comments: 0

By using concept of complex number show that tan 5θ=((tan^5 θ−10tan^3 θ+5tan θ)/(5tan^4 θ−10tan^2 θ+1))

$${By}\:{using}\:{concept}\:{of}\:{complex} \\ $$$${number} \\ $$$${show}\:{that} \\ $$$$\mathrm{tan}\:\mathrm{5}\theta=\frac{\mathrm{tan}\:^{\mathrm{5}} \theta−\mathrm{10tan}\:^{\mathrm{3}} \theta+\mathrm{5tan}\:\theta}{\mathrm{5tan}\:^{\mathrm{4}} \theta−\mathrm{10tan}\:^{\mathrm{2}} \theta+\mathrm{1}} \\ $$

Question Number 226779 Answers: 1 Comments: 0

By using De Moivres theorm simplify (a)(((cos (π/2)−isin (π/2))(cos (π/3)+isin (π/3)))/(cos (π/3)−isin (π/3))) (b)((cos (π/8)+isin (π/8))/(cos (π/6)+isin (π/6)))

$${By}\:{using}\:{De}\:{Moivres}\:{theorm} \\ $$$${simplify} \\ $$$$\left({a}\right)\frac{\left(\mathrm{cos}\:\frac{\pi}{\mathrm{2}}−{i}\mathrm{sin}\:\frac{\pi}{\mathrm{2}}\right)\left(\mathrm{cos}\:\frac{\pi}{\mathrm{3}}+{i}\mathrm{sin}\:\frac{\pi}{\mathrm{3}}\right)}{\mathrm{cos}\:\frac{\pi}{\mathrm{3}}−{i}\mathrm{sin}\:\frac{\pi}{\mathrm{3}}} \\ $$$$\left({b}\right)\frac{\mathrm{cos}\:\frac{\pi}{\mathrm{8}}+{i}\mathrm{sin}\:\frac{\pi}{\mathrm{8}}}{\mathrm{cos}\:\frac{\pi}{\mathrm{6}}+{i}\mathrm{sin}\:\frac{\pi}{\mathrm{6}}} \\ $$

Question Number 226778 Answers: 0 Comments: 0

Solve the following D.E (a) (dy/dx)+2y=xy^2 (b)3(dy/dx)+3(y/x)=2x^4 y^4

$${Solve}\:{the}\:{following}\:{D}.{E} \\ $$$$\left({a}\right)\:\frac{{dy}}{{dx}}+\mathrm{2}{y}={xy}^{\mathrm{2}} \\ $$$$\left({b}\right)\mathrm{3}\frac{{dy}}{{dx}}+\mathrm{3}\frac{{y}}{{x}}=\mathrm{2}{x}^{\mathrm{4}} {y}^{\mathrm{4}} \\ $$

Question Number 226777 Answers: 0 Comments: 0

Show that ∫_0 ^1 x^2 (1+x^2 )^(−1) dx=((4−π)/4) Hence by using Simpson^′ s rule find the value of π correct to 4 decimal places

$${Show}\:{that} \\ $$$$\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}} \left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{−\mathrm{1}} {dx}=\frac{\mathrm{4}−\pi}{\mathrm{4}} \\ $$$${Hence}\:{by}\:{using}\:{Simpson}^{'} {s} \\ $$$${rule}\:{find}\:{the}\:{value}\:\:{of}\:\pi \\ $$$${correct}\:{to}\:\mathrm{4}\:{decimal}\:{places} \\ $$

Question Number 226776 Answers: 0 Comments: 0

Approximate ∫_0 ^1 xe^x^2 dx with 6 ordinates. Use both rules Simpsons and Trapozoidal rules,hence evaluate and calculate the percentage error commetted for each case.Give comments

$${Approximate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {xe}^{{x}^{\mathrm{2}} } {dx}\:{with}\:\mathrm{6}\:{ordinates}. \\ $$$${Use}\:{both}\:{rules}\:{Simpsons}\:{and} \\ $$$${Trapozoidal}\:{rules},{hence}\:{evaluate}\:{and} \\ $$$${calculate}\:{the}\:{percentage}\:{error} \\ $$$${commetted}\:{for}\:{each}\:{case}.{Give}\:{comments} \\ $$$$ \\ $$

Question Number 226775 Answers: 0 Comments: 0

Prove that (a−b)(a−c)(a−d)(b−c)(b−d)(c−d) divisible by 12

$${Prove}\:{that}\:\left({a}−{b}\right)\left({a}−{c}\right)\left({a}−{d}\right)\left({b}−{c}\right)\left({b}−{d}\right)\left({c}−{d}\right)\:{divisible}\:{by}\:\mathrm{12} \\ $$

Question Number 226771 Answers: 2 Comments: 0

Question Number 226770 Answers: 2 Comments: 0

Question Number 226766 Answers: 1 Comments: 0

Question Number 226755 Answers: 2 Comments: 0

Question Number 226745 Answers: 1 Comments: 2

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: 7

Question Number 226732 Answers: 1 Comments: 0

Question Number 226728 Answers: 2 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: 1 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 )=?

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

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