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AllQuestion and Answers: Page 77

Question Number 205574 Answers: 1 Comments: 1

S=(1/(2!))−(1/(3!))+(1/(4!))−(1/(5!))... S=?

$${S}=\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{4}!}−\frac{\mathrm{1}}{\mathrm{5}!}... \\ $$$${S}=? \\ $$

Question Number 205562 Answers: 2 Comments: 0

Question Number 205551 Answers: 1 Comments: 0

what is the decomposition into cycles with disjoints support of c^k , where c=(123...n) ?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{decomposition}\:\mathrm{into}\:\mathrm{cycles} \\ $$$$\mathrm{with}\:\mathrm{disjoints}\:\mathrm{support}\:\mathrm{of}\:\mathrm{c}^{\mathrm{k}} ,\:\mathrm{where}\:\mathrm{c}=\left(\mathrm{123}...\mathrm{n}\right)\:? \\ $$

Question Number 205558 Answers: 1 Comments: 0

∫_0 ^(π/2) ((sin^2 4θ )/(sin^2 θ ))dθ = ?

$$\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \:\frac{\mathrm{sin}^{\mathrm{2}} \mathrm{4}\theta\:}{\mathrm{sin}^{\mathrm{2}} \theta\:}{d}\theta\:\:=\:\:\:? \\ $$

Question Number 205559 Answers: 2 Comments: 0

Question. (math analysis) (X ,d ) is a metric space and (p_n )_(n=1) ^∞ is a sequence in X. (p_n )_(n=1) ^( ∞) is cauchy if and only if lim_(N→∞) diam (E_N )=0. where , E_N = { p_N , p_(N+1) , ...} diam E:=sup{d(x,y)∣x,y ∈E }

$$ \\ $$$$\:\:\:{Question}.\:\left({math}\:{analysis}\right) \\ $$$$\:\:\left({X}\:,{d}\:\right)\:{is}\:{a}\:{metric}\:{space}\:{and} \\ $$$$\:\:\left({p}_{{n}} \right)_{{n}=\mathrm{1}} ^{\infty} \:{is}\:{a}\:{sequence}\:{in}\:{X}. \\ $$$$\:\:\:\left({p}_{{n}} \right)_{{n}=\mathrm{1}} ^{\:\infty} {is}\:{cauchy}\:{if}\:{and}\:\:{only}\:{if} \\ $$$$\:\:\:\mathrm{lim}_{\mathrm{N}\rightarrow\infty} {diam}\:\left({E}_{\mathrm{N}} \right)=\mathrm{0}. \\ $$$$\:\:{where}\:,\:{E}_{{N}} \:=\:\left\{\:{p}_{{N}} \:,\:{p}_{{N}+\mathrm{1}} \:,\:...\right\} \\ $$$$\:\:{diam}\:{E}:={sup}\left\{{d}\left({x},{y}\right)\mid{x},{y}\:\in{E}\:\right\} \\ $$$$\:\:\:\: \\ $$

Question Number 205545 Answers: 4 Comments: 1

Question Number 205580 Answers: 1 Comments: 2

lim_(n→∞) (((2n+1)(2n+3)...(4n+1))/((2n)(2n+2)...(4n))) = ?

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)...\left(\mathrm{4}{n}+\mathrm{1}\right)}{\left(\mathrm{2}{n}\right)\left(\mathrm{2}{n}+\mathrm{2}\right)...\left(\mathrm{4}{n}\right)}\:\:=\:\:? \\ $$

Question Number 205577 Answers: 1 Comments: 5

is ∞ a real number?

$$\mathrm{is}\:\infty\:\mathrm{a}\:\mathrm{real}\:\mathrm{number}? \\ $$

Question Number 205534 Answers: 1 Comments: 0

Find: lim_(n→∞) ∫_0 ^( 1) n x^n e^x^2 dx = ?

$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{n}\:\mathrm{x}^{\boldsymbol{\mathrm{n}}} \:\mathrm{e}^{\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \:\mathrm{dx}\:=\:? \\ $$

Question Number 205535 Answers: 2 Comments: 0

Question Number 205530 Answers: 1 Comments: 0

Question Number 205528 Answers: 1 Comments: 0

Let ∀x ∈ A → x ∈ R And card(A) > card N Prove that: card(A′) > card N

$$\mathrm{Let}\:\:\:\forall\mathrm{x}\:\in\:\mathrm{A}\:\rightarrow\:\mathrm{x}\:\in\:\mathbb{R} \\ $$$$\mathrm{And}\:\:\:\mathrm{card}\left(\mathrm{A}\right)\:>\:\mathrm{card}\:\mathrm{N} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{card}\left(\mathrm{A}'\right)\:>\:\mathrm{card}\:\mathrm{N} \\ $$

Question Number 205527 Answers: 3 Comments: 0

If the roots of ax^2 + bx + c = 0 are one another′s cube then show that (b^2 − 2ac)^2 = ac(a + c)^2 .

$$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{are}\:\mathrm{one} \\ $$$$\mathrm{another}'\mathrm{s}\:\mathrm{cube}\:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$$\left({b}^{\mathrm{2}} \:−\:\mathrm{2}{ac}\right)^{\mathrm{2}} \:=\:{ac}\left({a}\:+\:{c}\right)^{\mathrm{2}} . \\ $$

Question Number 205517 Answers: 1 Comments: 0

Question Number 205516 Answers: 0 Comments: 0

Σ_(h=1) ^∞ ((𝛇(2h)−1)/h) = .....? Σ_(h=1) ^∞ (𝛇(2h+1)−1)=......? pls help me

$$\underset{{h}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\boldsymbol{\zeta}\left(\mathrm{2}{h}\right)−\mathrm{1}}{{h}}\:=\:.....? \\ $$$$\underset{{h}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left(\boldsymbol{\zeta}\left(\mathrm{2}{h}+\mathrm{1}\right)−\mathrm{1}\right)=......? \\ $$$$\mathrm{pls}\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 205515 Answers: 0 Comments: 0

what is the decomposition into cycles with disjoints support of c^k , where c=(123...n) ?

Question Number 205514 Answers: 0 Comments: 3

Quelle est la decomposition en cycles a support disjoints de c^k , ou c=(1 2 3 ... n) ?

$$\mathrm{Quelle}\:\mathrm{est}\:\mathrm{la}\:\mathrm{decomposition}\:\mathrm{en}\:\mathrm{cycles} \\ $$$$\mathrm{a}\:\mathrm{support}\:\mathrm{disjoints}\:\mathrm{de}\:\mathrm{c}^{\mathrm{k}} \:,\:\mathrm{ou}\:\mathrm{c}=\left(\mathrm{1}\:\mathrm{2}\:\mathrm{3}\:...\:\mathrm{n}\right)\:? \\ $$

Question Number 205507 Answers: 1 Comments: 1

Question Number 205506 Answers: 1 Comments: 0

∫_0 ^1 (√(1−x^4 ))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 205502 Answers: 2 Comments: 0

If two roots of ax^2 + bx + c = 0 are α and β then (1/((aα^2 + c)^2 )) + (1/((aβ^2 + c)^2 )) = ?

$$\mathrm{If}\:\mathrm{two}\:\mathrm{roots}\:\mathrm{of}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{are}\:\alpha\:\mathrm{and}\: \\ $$$$\beta\:\mathrm{then}\:\frac{\mathrm{1}}{\left({a}\alpha^{\mathrm{2}} \:+\:{c}\right)^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\left({a}\beta^{\mathrm{2}} \:+\:{c}\right)^{\mathrm{2}} }\:=\:? \\ $$

Question Number 205496 Answers: 1 Comments: 0

Question Number 205492 Answers: 2 Comments: 0

Question Number 205490 Answers: 1 Comments: 0

If,f(x)= (√(2 + x)) + a (√(x − 1)) is monotone function . find the range of ” a ”

$$ \\ $$$$\:\:\:\:{If},{f}\left({x}\right)=\:\sqrt{\mathrm{2}\:+\:{x}}\:+\:{a}\:\sqrt{{x}\:−\:\mathrm{1}}\: \\ $$$$\:\:\:\:{is}\:{monotone}\:{function}\:. \\ $$$$\:\:\:\:{find}\:{the}\:{range}\:{of}\:\:''\:{a}\:'' \\ $$$$ \\ $$

Question Number 205471 Answers: 2 Comments: 0

Solve the equation: (x/(21))+(x/(77))+(x/(165))+(x/(285))=200

$${Solve}\:{the}\:{equation}:\:\frac{{x}}{\mathrm{21}}+\frac{{x}}{\mathrm{77}}+\frac{{x}}{\mathrm{165}}+\frac{{x}}{\mathrm{285}}=\mathrm{200} \\ $$

Question Number 205461 Answers: 2 Comments: 1

Question Number 205460 Answers: 1 Comments: 0

If 3cosx = 8sin(30° − x) Find: tanx = ?

$$\mathrm{If}\:\:\mathrm{3cosx}\:=\:\mathrm{8sin}\left(\mathrm{30}°\:−\:\mathrm{x}\right) \\ $$$$\mathrm{Find}:\:\:\mathrm{tanx}\:=\:? \\ $$

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