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Question Number 14104 Answers: 0 Comments: 0

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Question Number 14100 Answers: 0 Comments: 0

Slove ▽Φ

$${Slove}\:\bigtriangledown\Phi \\ $$

Question Number 14079 Answers: 0 Comments: 2

Question Number 14078 Answers: 3 Comments: 4

Question Number 14077 Answers: 2 Comments: 0

Question Number 14073 Answers: 1 Comments: 4

Question Number 14071 Answers: 2 Comments: 1

Solve the Partial fraction ((3x^4 − 9x^3 + 16x^2 + 9x + 13)/((x − 1)^2 (x^2 + 2x − 2)^2 ))

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{Partial}\:\mathrm{fraction}\: \\ $$$$\frac{\mathrm{3x}^{\mathrm{4}} \:−\:\mathrm{9x}^{\mathrm{3}} \:+\:\mathrm{16x}^{\mathrm{2}} \:+\:\mathrm{9x}\:+\:\mathrm{13}}{\left(\mathrm{x}\:−\:\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2x}\:−\:\mathrm{2}\right)^{\mathrm{2}} } \\ $$

Question Number 14047 Answers: 0 Comments: 13

S=1+i−1−i+1+... (1/i)=−i S=i(−i+1+i−1−i+1+...) S=i(−i+S) S=1+iS S(1−i)=1 ∴ S=(1/(1−i)) a) Is this correct? b) Do there exist any other sequences in the form of: S=(a_1 +...+a_n )+(a_1 +...+a_n )+... S=(a_1 +...+a_n )(1+1+...+1_(m times) ) ⇒S=Σ_(i=1) ^(m→∞) Σ_(j=1) ^n a_j where a_(t+1) =ba_t , a_1 =ba_n I′m very interested in these sequences

$${S}=\mathrm{1}+{i}−\mathrm{1}−{i}+\mathrm{1}+... \\ $$$$\frac{\mathrm{1}}{{i}}=−{i} \\ $$$${S}={i}\left(−{i}+\mathrm{1}+{i}−\mathrm{1}−{i}+\mathrm{1}+...\right) \\ $$$${S}={i}\left(−{i}+{S}\right) \\ $$$${S}=\mathrm{1}+{iS} \\ $$$${S}\left(\mathrm{1}−{i}\right)=\mathrm{1} \\ $$$$\therefore\:{S}=\frac{\mathrm{1}}{\mathrm{1}−{i}} \\ $$$$\: \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Is}\:\mathrm{this}\:\mathrm{correct}? \\ $$$$\left.\mathrm{b}\right)\:\mathrm{Do}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{any}\:\mathrm{other}\:\mathrm{sequences} \\ $$$$\:\:\:\:\:\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\mathrm{of}: \\ $$$${S}=\left({a}_{\mathrm{1}} +...+{a}_{{n}} \right)+\left({a}_{\mathrm{1}} +...+{a}_{{n}} \right)+... \\ $$$${S}=\left({a}_{\mathrm{1}} +...+{a}_{{n}} \right)\left(\underset{{m}\:\mathrm{times}} {\mathrm{1}+\mathrm{1}+...+\mathrm{1}}\right) \\ $$$$\Rightarrow{S}=\underset{{i}=\mathrm{1}} {\overset{{m}\rightarrow\infty} {\sum}}\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}{a}_{{j}} \\ $$$$\mathrm{where}\:{a}_{{t}+\mathrm{1}} ={ba}_{{t}} ,\:\:{a}_{\mathrm{1}} ={ba}_{{n}} \\ $$$$\: \\ $$$$\mathrm{I}'\mathrm{m}\:\mathrm{very}\:\mathrm{interested}\:\mathrm{in}\:\mathrm{these}\:\mathrm{sequences} \\ $$

Question Number 14046 Answers: 2 Comments: 0

Calculate: (√ω)

$$\mathrm{Calculate}:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\omega} \\ $$

Question Number 14042 Answers: 0 Comments: 2

Can we express ω^(1/2) in terms of whole powers of ω?

$$\mathrm{Can}\:\mathrm{we}\:\mathrm{express}\:\:\omega^{\mathrm{1}/\mathrm{2}} \:\mathrm{in}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{whole}\:\mathrm{powers}\:\mathrm{of}\:\omega? \\ $$

Question Number 14030 Answers: 1 Comments: 0

The general solution of equation tan x tan 4x = 1 is (1) (2n + 1)(π/(10)) , n ∈ Z − {n : n = 5k +2; k ∈ Z} (2) (4n − 1)(π/(10)) , n ∈ Z (3) ((nπ)/(10)) , n ∈ Z (4) 2nπ + (π/(10)) , n ∈ Z

$$\mathrm{The}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{equation} \\ $$$$\mathrm{tan}\:{x}\:\mathrm{tan}\:\mathrm{4}{x}\:=\:\mathrm{1}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\left(\mathrm{2}{n}\:+\:\mathrm{1}\right)\frac{\pi}{\mathrm{10}}\:,\:{n}\:\in\:{Z}\:−\:\left\{{n}\::\:{n}\:=\:\mathrm{5}{k}\:+\mathrm{2};\:{k}\:\in\:{Z}\right\} \\ $$$$\left(\mathrm{2}\right)\:\left(\mathrm{4}{n}\:−\:\mathrm{1}\right)\frac{\pi}{\mathrm{10}}\:,\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{3}\right)\:\frac{{n}\pi}{\mathrm{10}}\:,\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{2}{n}\pi\:+\:\frac{\pi}{\mathrm{10}}\:,\:{n}\:\in\:{Z} \\ $$

Question Number 14028 Answers: 0 Comments: 0