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Question Number 80374 Answers: 0 Comments: 5

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Question Number 80341 Answers: 1 Comments: 0

A particle moves round the polar curve r = a(1 + cos θ) with constant angular velocity ω . Find the transverse component of the velocity.

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{round}\:\mathrm{the}\:\mathrm{polar}\:\mathrm{curve} \\ $$$${r}\:=\:{a}\left(\mathrm{1}\:+\:\mathrm{cos}\:\theta\right)\:\mathrm{with}\:\mathrm{constant}\:\mathrm{angular}\: \\ $$$$\mathrm{velocity}\:\omega\:.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{transverse}\:\mathrm{component} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{velocity}. \\ $$

Question Number 80340 Answers: 1 Comments: 0

If P = ((a,b,c,d),(c,d,a,b) ) , Q = ((a,b,c,d),(b,a,d,c) ) are permutations of the elements (a,b,c,d), then QP ≡

$$\mathrm{If}\:{P}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{c}}&{{d}}&{{a}}&{{b}}\end{pmatrix}\:\:,\:{Q}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{b}}&{{a}}&{{d}}&{{c}}\end{pmatrix}\:\mathrm{are} \\ $$$$\mathrm{permutations}\:\mathrm{of}\:\mathrm{the}\:\mathrm{elements}\:\left({a},{b},{c},{d}\right),\:\mathrm{then}\: \\ $$$${QP}\:\equiv \\ $$$$\: \\ $$

Question Number 80334 Answers: 0 Comments: 1

let f∈L^1 (R) let u_n = ∫_a ^b f(t)sin(nt)dt , v_n =∫_a ^b ((f(t))/t)sin(nt) 1)Prove that lim_(n→∞) u_n =0 2)Deduce in term of a,b,f(0) the value of lim_(n→∞) v_n

$$\:{let}\:\:\:{f}\in{L}^{\mathrm{1}} \left(\mathbb{R}\right)\:\:\: \\ $$$${let}\:\:{u}_{{n}} =\:\int_{{a}} ^{{b}} {f}\left({t}\right){sin}\left({nt}\right){dt}\:,\:{v}_{{n}} =\int_{{a}} ^{{b}} \frac{{f}\left({t}\right)}{{t}}{sin}\left({nt}\right)\: \\ $$$$\left.\mathrm{1}\right){Prove}\:{that}\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{u}_{{n}} =\mathrm{0} \\ $$$$\left.\mathrm{2}\right){Deduce}\:\:{in}\:{term}\:{of}\:{a},{b},{f}\left(\mathrm{0}\right)\:{the}\:{value}\:{of}\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{v}_{{n}} \:\: \\ $$

Question Number 80332 Answers: 0 Comments: 1

let α ∈R and a_n =Σ_(k=1) ^n ((sin(kα))/(n+k)) Find lim_(n→∞) a_n

$$\:\:{let}\:\alpha\:\in\mathbb{R}\:\:{and}\:\:\:\:{a}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{sin}\left({k}\alpha\right)}{{n}+{k}} \\ $$$${Find}\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:{a}_{{n}} \: \\ $$

Question Number 80346 Answers: 0 Comments: 0

Question Number 80343 Answers: 0 Comments: 3

lim_(x→0) ((ln(tan x+1)−sin x)/(xsin x))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{ln}\left(\mathrm{tan}\:{x}+\mathrm{1}\right)−\mathrm{sin}\:{x}}{{x}\mathrm{sin}\:{x}} \\ $$

Question Number 80312 Answers: 1 Comments: 17

Question Number 80306 Answers: 0 Comments: 1

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Question Number 80347 Answers: 1 Comments: 6

let x and y be positif real number such that 1≤x+y≤9 and x≤2y≤3x. what is the largest value of ((9−y)/(9−x))

$${let}\:{x}\:{and}\:{y}\:{be}\:{positif}\:{real}\:{number} \\ $$$${such}\:{that}\:\mathrm{1}\leqslant{x}+{y}\leqslant\mathrm{9}\:{and} \\ $$$${x}\leqslant\mathrm{2}{y}\leqslant\mathrm{3}{x}.\:{what}\:{is}\:{the}\: \\ $$$${largest}\:{value}\:{of}\:\:\:\frac{\mathrm{9}−{y}}{\mathrm{9}−{x}} \\ $$$$ \\ $$

Question Number 80296 Answers: 0 Comments: 3

what is the value of lim_(x→−∞ ) e^((6x^2 +x)/(3x+5)) ? 0 or ∞ ?

$${what}\:{is}\:{the}\:{value}\:{of}\: \\ $$$$\underset{{x}\rightarrow−\infty\:} {\mathrm{lim}}\:{e}^{\frac{\mathrm{6}{x}^{\mathrm{2}} +{x}}{\mathrm{3}{x}+\mathrm{5}}} \:? \\ $$$$\mathrm{0}\:{or}\:\infty\:? \\ $$

Question Number 80293 Answers: 0 Comments: 12

Find all functions that satisfy to (E): ∀ x∈R xf(x)+∫_0 ^x f(x−t)cos(2t)dt=sin(2x)

$${Find}\:{all}\:{functions}\:{that}\:\:{satisfy}\:{to}\:\: \\ $$$$\left({E}\right):\:\forall\:{x}\in\mathbb{R}\:\:\:\:\:\:{xf}\left({x}\right)+\int_{\mathrm{0}} ^{{x}} {f}\left({x}−{t}\right){cos}\left(\mathrm{2}{t}\right){dt}={sin}\left(\mathrm{2}{x}\right) \\ $$$$\: \\ $$

Question Number 80284 Answers: 0 Comments: 0

Question Number 80276 Answers: 1 Comments: 1

lim_(x→0) ((e^x −e^(−x) −2x)/(x−sin(x)))=L >0 , L∈R find L with out using hopital and Taylor methods

$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{{e}^{{x}} −{e}^{−{x}} −\mathrm{2}{x}}{{x}−{sin}\left({x}\right)}={L}\:\:>\mathrm{0}\:,\:{L}\in{R} \\ $$$${find}\:{L} \\ $$$$ \\ $$$${with}\:{out}\:{using}\:{hopital}\:{and}\:{Taylor}\:{methods} \\ $$

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if x+(1/x)=a (a∈R) find x^n +(1/x^n )=? (n∈N)

$${if}\:{x}+\frac{\mathrm{1}}{{x}}={a}\:\left({a}\in\mathbb{R}\right) \\ $$$${find}\:{x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }=? \\ $$$$\left({n}\in\mathbb{N}\right) \\ $$

Question Number 80237 Answers: 1 Comments: 5

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Question Number 80227 Answers: 0 Comments: 5

how to prove ∫_0 ^1 x^n (1−x)^(m ) dx = ((m! ×n!)/((m+n)!)) via Gamma function

$${how}\:{to}\:{prove} \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{x}^{{n}} \:\left(\mathrm{1}−{x}\right)^{{m}\:} \:{dx}\:=\:\frac{{m}!\:×{n}!}{\left({m}+{n}\right)!} \\ $$$${via}\:{Gamma}\:{function} \\ $$

Question Number 80222 Answers: 1 Comments: 2

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