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Question Number 192340 Answers: 1 Comments: 0

Prove that the order of any permuta− tion θ is the least common multiple of the length of its disjoint cycles. hi

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{order}\:\mathrm{of}\:\mathrm{any}\:\mathrm{permuta}− \\ $$$$\mathrm{tion}\:\theta\:\mathrm{is}\:\mathrm{the}\:\mathrm{least}\:\mathrm{common}\:\mathrm{multiple} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{its}\:\mathrm{disjoint}\:\mathrm{cycles}. \\ $$$$ \\ $$$$\:\mathrm{hi} \\ $$

Question Number 192339 Answers: 1 Comments: 0

Express as the product of disjoint cycle the permutation a) θ(1)=4 θ(2)=6 θ(1)=5 θ(4)=1 θ(5)=3 θ(6)=2 b) (1 6 3)(1 3 5 7)(6 7)(1 2 3 4 5) c) (1 2 3 4 5)(6 7)(1 3 5 7) Find the order of each of them help!

$$\mathrm{Express}\:\mathrm{as}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{disjoint}\: \\ $$$$\mathrm{cycle}\:\mathrm{the}\:\mathrm{permutation} \\ $$$$\left.\mathrm{a}\right)\:\theta\left(\mathrm{1}\right)=\mathrm{4}\:\:\theta\left(\mathrm{2}\right)=\mathrm{6}\:\:\theta\left(\mathrm{1}\right)=\mathrm{5}\:\:\theta\left(\mathrm{4}\right)=\mathrm{1} \\ $$$$\theta\left(\mathrm{5}\right)=\mathrm{3}\:\:\theta\left(\mathrm{6}\right)=\mathrm{2} \\ $$$$ \\ $$$$\left.\mathrm{b}\right)\:\left(\mathrm{1}\:\mathrm{6}\:\mathrm{3}\right)\left(\mathrm{1}\:\mathrm{3}\:\mathrm{5}\:\mathrm{7}\right)\left(\mathrm{6}\:\mathrm{7}\right)\left(\mathrm{1}\:\mathrm{2}\:\mathrm{3}\:\mathrm{4}\:\mathrm{5}\right) \\ $$$$ \\ $$$$\left.\mathrm{c}\right)\:\left(\mathrm{1}\:\mathrm{2}\:\mathrm{3}\:\mathrm{4}\:\mathrm{5}\right)\left(\mathrm{6}\:\mathrm{7}\right)\left(\mathrm{1}\:\mathrm{3}\:\mathrm{5}\:\mathrm{7}\right) \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{order}\:\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{them} \\ $$$$ \\ $$$$\mathrm{help}! \\ $$

Question Number 192338 Answers: 2 Comments: 0

y= ((((lim_(h→0) (((x+h)^3 −x^3 )/h))(Σ_(n=0) ^∞ (x^(n+1) /(n+1))))/(∫_0 ^( x) lnt dt))) (dy/dx)?

$${y}=\:\left(\frac{\left(\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left({x}+{h}\right)^{\mathrm{3}} −{x}^{\mathrm{3}} }{{h}}\right)\left(\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{{n}+\mathrm{1}} }{{n}+\mathrm{1}}\right)}{\int_{\mathrm{0}} ^{\:{x}} {lnt}\:{dt}}\right) \\ $$$$ \\ $$$$\frac{{dy}}{{dx}}? \\ $$

Question Number 192336 Answers: 1 Comments: 0

Question Number 192331 Answers: 0 Comments: 0

Question Number 192330 Answers: 0 Comments: 0

Question Number 192325 Answers: 1 Comments: 0

Question Number 192345 Answers: 1 Comments: 0

Question Number 192344 Answers: 0 Comments: 4

Question Number 192346 Answers: 1 Comments: 0

Question Number 192350 Answers: 2 Comments: 0

Question Number 192349 Answers: 1 Comments: 0

Question Number 192348 Answers: 2 Comments: 0

Question Number 192299 Answers: 2 Comments: 0

Question Number 192297 Answers: 2 Comments: 0

Question Number 192288 Answers: 1 Comments: 0

Question Number 192289 Answers: 1 Comments: 0

∫_(−e) ^e ((sin x)/(sec^2 x+1)) dx =?

$$\:\:\:\:\:\:\:\:\underset{−\mathrm{e}} {\overset{\mathrm{e}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}+\mathrm{1}}\:\mathrm{dx}\:=? \\ $$

Question Number 192286 Answers: 1 Comments: 0

Determine whether f(x)=(1/x)(2x^2 +1)is: 1.A function 2. injective 3. surjective 4. bijective

$$\mathrm{Determine}\:\mathrm{whether}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{x}}\left(\mathrm{2x}^{\mathrm{2}} +\mathrm{1}\right)\mathrm{is}: \\ $$$$\mathrm{1}.\mathrm{A}\:\mathrm{function} \\ $$$$\mathrm{2}.\:\mathrm{injective} \\ $$$$\mathrm{3}.\:\mathrm{surjective} \\ $$$$\mathrm{4}.\:\mathrm{bijective} \\ $$

Question Number 192282 Answers: 1 Comments: 0

find the value of tan (π/9) + 4sin (π/9) = ?

$$\:\:\:{find}\:{the}\:{value}\:{of} \\ $$$$\:\:\:\:\mathrm{tan}\:\frac{\pi}{\mathrm{9}}\:+\:\mathrm{4sin}\:\frac{\pi}{\mathrm{9}}\:=\:? \\ $$

Question Number 192281 Answers: 0 Comments: 0

help me proving this f:R→R dan c∈R lim_(x→c) f(x)=L ⇔ lim_(c→0) f(x+c)=L

$$ \\ $$$$ \\ $$$$\:{help}\:{me}\:{proving}\:{this} \\ $$$$\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:{dan}\:{c}\in\mathbb{R} \\ $$$$\:\underset{{x}\rightarrow{c}} {\mathrm{lim}}\:{f}\left({x}\right)={L}\:\Leftrightarrow\:\underset{{c}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{f}\left({x}+{c}\right)={L} \\ $$$$\: \\ $$$$ \\ $$

Question Number 192280 Answers: 2 Comments: 0

Question Number 192278 Answers: 1 Comments: 2

S=arctan((2/1^2 ))+artan((2/2^2 ))+........

$${S}={arctan}\left(\frac{\mathrm{2}}{\mathrm{1}^{\mathrm{2}} }\right)+{artan}\left(\frac{\mathrm{2}}{\mathrm{2}^{\mathrm{2}} }\right)+........ \\ $$

Question Number 192277 Answers: 1 Comments: 0

Let a_1 , a_2 , a_3 ,..., a_n be real numbers such that: (√a_1 ) + (√(a_2 −1 )) +(√(a_3 −2 )) +...+(√(a_n −(n−1) ))=(1/2)(a_1 +a_2 +a_3 +...+a_n )−((n(n−3))/4) Then find the value of [ Σ_(i=1) ^(100) (a_i )].

$$ \\ $$$${Let}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:{a}_{\mathrm{3}} ,...,\:{a}_{{n}} \:{be}\:{real}\:{numbers}\:{such}\:{that}: \\ $$$$\sqrt{{a}_{\mathrm{1}} }\:+\:\sqrt{{a}_{\mathrm{2}} −\mathrm{1}\:\:}\:+\sqrt{{a}_{\mathrm{3}} −\mathrm{2}\:}\:+...+\sqrt{{a}_{{n}} −\left({n}−\mathrm{1}\right)\:}=\frac{\mathrm{1}}{\mathrm{2}}\left({a}_{\mathrm{1}} +{a}_{\mathrm{2}} +{a}_{\mathrm{3}} +...+{a}_{{n}} \right)−\frac{{n}\left({n}−\mathrm{3}\right)}{\mathrm{4}} \\ $$$$\boldsymbol{{Then}}\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\left[\:\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{\mathrm{100}} {\sum}}\left(\boldsymbol{{a}}_{\boldsymbol{{i}}} \right)\right]. \\ $$

Question Number 192276 Answers: 1 Comments: 0

lim_(n→∞) (Σ_(k=0) ^n [((k(n−k)!+(k+1))/((k+1)!(n−k)!))])

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left[\frac{{k}\left({n}−{k}\right)!+\left({k}+\mathrm{1}\right)}{\left({k}+\mathrm{1}\right)!\left({n}−{k}\right)!}\right]\right) \\ $$

Question Number 192275 Answers: 2 Comments: 0

2009^3^(2016n+2013) +2010^2^(2016n+2013) ≡x mod(11) where n is any integer ≥0

$$\mathrm{2009}^{\mathrm{3}^{\mathrm{2016}{n}+\mathrm{2013}} } +\mathrm{2010}^{\mathrm{2}^{\mathrm{2016}{n}+\mathrm{2013}} } \equiv{x}\:{mod}\left(\mathrm{11}\right)\:{where}\:{n}\:{is}\:{any}\:{integer}\:\geq\mathrm{0} \\ $$$$ \\ $$

Question Number 192274 Answers: 1 Comments: 0

prove that lim_(n→∞) (Σ_(k=1) ^n (n^2 /( (√(n^6 +k)))))=1

$${prove}\:{that}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{n}^{\mathrm{2}} }{\:\sqrt{{n}^{\mathrm{6}} +{k}}}\right)=\mathrm{1} \\ $$$$ \\ $$$$ \\ $$

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