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AllQuestion and Answers: Page 1208

Question Number 94708 Answers: 1 Comments: 1

Question Number 94706 Answers: 2 Comments: 0

Question Number 94705 Answers: 0 Comments: 1

a set X had one more subset than set Y. If X has 8 more subsets than Y. Find the number if element in the set X.

$$\mathrm{a}\:\mathrm{set}\:\mathrm{X}\:\mathrm{had}\:\mathrm{one}\:\mathrm{more}\:\mathrm{subset}\:\mathrm{than}\:\mathrm{set}\:\mathrm{Y}. \\ $$$$\mathrm{If}\:\mathrm{X}\:\mathrm{has}\:\mathrm{8}\:\mathrm{more}\:\mathrm{subsets}\:\mathrm{than}\:\mathrm{Y}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{if}\:\mathrm{element}\:\mathrm{in}\:\mathrm{the}\:\mathrm{set}\:\mathrm{X}. \\ $$

Question Number 94701 Answers: 0 Comments: 3

what is the volume of x^2 +y^2 +z^2 =2

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{2} \\ $$$$ \\ $$

Question Number 94698 Answers: 1 Comments: 0

Question Number 94693 Answers: 0 Comments: 1

Question Number 94690 Answers: 0 Comments: 4

Question Number 94679 Answers: 2 Comments: 2

Question Number 94676 Answers: 0 Comments: 0

Find the supremum and infimum of A = { n ∣ 3 + (2/n) , n ∈ R }

$${Find}\:\:{the}\:\:{supremum}\:\:{and}\:\:{infimum}\:\:{of}\:\: \\ $$$${A}\:\:=\:\:\left\{\:{n}\:\mid\:\:\mathrm{3}\:+\:\frac{\mathrm{2}}{{n}}\:\:,\:\:{n}\:\in\:\:\mathbb{R}\:\:\right\} \\ $$

Question Number 94664 Answers: 0 Comments: 9

App updates: • Improvement in handling image upload and display (small width, large height cases) • Editor can be opened in landscape mode. • Added ability to save thread to device. ′Save to Device′ • An automatic comment is added to a post to visit referenced question Q/q followed by number ex. 94644 on same line

$$\mathrm{App}\:\mathrm{updates}: \\ $$$$\bullet\:\mathrm{Improvement}\:\mathrm{in}\:\mathrm{handling}\:\mathrm{image} \\ $$$$\:\:\:\:\mathrm{upload}\:\mathrm{and}\:\mathrm{display}\:\left(\mathrm{small}\:\mathrm{width},\right. \\ $$$$\left.\:\:\:\:\mathrm{large}\:\mathrm{height}\:\mathrm{cases}\right) \\ $$$$\bullet\:\mathrm{Editor}\:\mathrm{can}\:\mathrm{be}\:\mathrm{opened}\:\mathrm{in}\:\mathrm{landscape} \\ $$$$\:\:\:\:\mathrm{mode}. \\ $$$$\bullet\:\mathrm{Added}\:\mathrm{ability}\:\mathrm{to}\:\mathrm{save}\:\mathrm{thread}\:\mathrm{to} \\ $$$$\:\:\:\:\mathrm{device}.\:'\mathrm{Save}\:\mathrm{to}\:\mathrm{Device}' \\ $$$$\bullet\:\mathrm{An}\:\mathrm{automatic}\:\mathrm{comment}\:\mathrm{is}\:\mathrm{added} \\ $$$$\:\:\:\:\mathrm{to}\:\mathrm{a}\:\mathrm{post}\:\mathrm{to}\:\mathrm{visit}\:\mathrm{referenced}\:\mathrm{question} \\ $$$$\:\:\:\:\:\mathrm{Q}/\mathrm{q}\:\mathrm{followed}\:\mathrm{by}\:\mathrm{number}\:\mathrm{ex}.\:\mathrm{94644} \\ $$$$\:\:\:\:\:\mathrm{on}\:\mathrm{same}\:\mathrm{line} \\ $$

Question Number 94662 Answers: 1 Comments: 3

∫ (√(tan x+cot x)) dx = ?

$$\int\:\sqrt{\mathrm{tan}\:\mathrm{x}+\mathrm{cot}\:\mathrm{x}}\:\mathrm{dx}\:=\:? \\ $$

Question Number 94661 Answers: 0 Comments: 0

calculate Σ a_n x^n if a_n verify a_(n+1) =a_n +a_(n−1)

$${calculate}\:\Sigma\:{a}_{{n}} {x}^{{n}} \:{if}\:{a}_{{n}} \:{verify} \\ $$$${a}_{{n}+\mathrm{1}} ={a}_{{n}} \:+{a}_{{n}−\mathrm{1}} \\ $$

Question Number 94660 Answers: 0 Comments: 0

u_n =(1+(1/n^2 ))(1+(2/n^2 ))...(1+(n/n^2 )) find lim_(n→+∞) u_n

$${u}_{{n}} =\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)\left(\mathrm{1}+\frac{\mathrm{2}}{{n}^{\mathrm{2}} }\right)...\left(\mathrm{1}+\frac{{n}}{{n}^{\mathrm{2}} }\right) \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} {u}_{{n}} \\ $$

Question Number 94659 Answers: 1 Comments: 0

calculate lim_(n→+∞) ∫_0 ^∞ (1−(t/n))^n e^(−3t) dt

$${calculate}\:{lim}_{{n}\rightarrow+\infty} \int_{\mathrm{0}} ^{\infty} \:\left(\mathrm{1}−\frac{{t}}{{n}}\right)^{{n}} \:{e}^{−\mathrm{3}{t}} \:{dt} \\ $$

Question Number 94658 Answers: 0 Comments: 0

find lim_(n→+∞) ∫_0 ^1 (1−(t/n))^n arctan(1+nt)dt

$${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\left(\mathrm{1}−\frac{{t}}{{n}}\right)^{{n}} \:{arctan}\left(\mathrm{1}+{nt}\right){dt} \\ $$

Question Number 94657 Answers: 0 Comments: 0

let u_n =Σ_(k=1) ^n (1/((^p (√k)))) detetmine a equivalent of u_n (n→+∞)

$${let}\:{u}_{{n}} \:=\sum_{{k}=\mathrm{1}} ^{{n}} \frac{\mathrm{1}}{\left(^{{p}} \sqrt{{k}}\right)} \\ $$$${detetmine}\:{a}\:{equivalent}\:{of}\:{u}_{{n}} \\ $$$$\left({n}\rightarrow+\infty\right) \\ $$$$ \\ $$

Question Number 94655 Answers: 0 Comments: 0

solve (1+nz)^p +(1−nz)^p =0 n and p ontegr natural

$${solve}\:\left(\mathrm{1}+{nz}\right)^{{p}} +\left(\mathrm{1}−{nz}\right)^{{p}} \:=\mathrm{0} \\ $$$${n}\:{and}\:{p}\:{ontegr}\:{natural} \\ $$

Question Number 94654 Answers: 0 Comments: 0

prove that Σ_(i=1) ^n x_i y_i ≤(Σ_(i=1) ^n x_i ^2 )^(1/2) (Σ_(i=1) ^n y_i ^2 )^(1/2) x_i and y_i reals ≥0

$${prove}\:{that}\:\sum_{{i}=\mathrm{1}} ^{{n}} \:{x}_{{i}} {y}_{{i}} \leqslant\left(\sum_{{i}=\mathrm{1}} ^{{n}} {x}_{{i}} ^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \left(\sum_{{i}=\mathrm{1}} ^{{n}} {y}_{{i}} ^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$${x}_{{i}} \:{and}\:{y}_{{i}} \:{reals}\:\geqslant\mathrm{0} \\ $$

Question Number 94652 Answers: 0 Comments: 0

find lim_(ξ→0) ∫_0 ^1 ((sin(ξx))/((√(1+ξx^2 ))−(√(1−ξx^2 ))))dx

$${find}\:{lim}_{\xi\rightarrow\mathrm{0}} \:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\frac{{sin}\left(\xi{x}\right)}{\sqrt{\mathrm{1}+\xi{x}^{\mathrm{2}} }−\sqrt{\mathrm{1}−\xi{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 94650 Answers: 1 Comments: 1

let f(x) =(x+1)^9 e^(−3x) calculstr f^((7)) (0) and f^((5)) (1)

$${let}\:{f}\left({x}\right)\:=\left({x}+\mathrm{1}\right)^{\mathrm{9}} \:{e}^{−\mathrm{3}{x}} \\ $$$${calculstr}\:{f}^{\left(\mathrm{7}\right)} \left(\mathrm{0}\right)\:{and}\:{f}^{\left(\mathrm{5}\right)} \left(\mathrm{1}\right) \\ $$

Question Number 94649 Answers: 0 Comments: 0

calculate ∫_0 ^∞ e^(−x) lnx dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}} {lnx}\:{dx} \\ $$

Question Number 94648 Answers: 0 Comments: 0

find a equivslent for u_n =1 +2^α +3^α +....+n^α n→+∞ (α>0)

$${find}\:{a}\:{equivslent}\:{for} \\ $$$${u}_{{n}} =\mathrm{1}\:+\mathrm{2}^{\alpha} \:+\mathrm{3}^{\alpha} \:+....+{n}^{\alpha} \\ $$$${n}\rightarrow+\infty\:\:\:\:\:\:\:\:\:\left(\alpha>\mathrm{0}\right) \\ $$

Question Number 94635 Answers: 1 Comments: 0

A father with 8 children takes them 3 at a time to the Gardens, as often as he can without taking the same 3 children together more than once. The number of times each child will go to the garden is

$$\mathrm{A}\:\mathrm{father}\:\mathrm{with}\:\mathrm{8}\:\mathrm{children}\:\mathrm{takes}\:\mathrm{them} \\ $$$$\mathrm{3}\:\mathrm{at}\:\mathrm{a}\:\mathrm{time}\:\mathrm{to}\:\mathrm{the}\:\mathrm{Gardens},\:\mathrm{as}\:\mathrm{often}\:\mathrm{as} \\ $$$$\mathrm{he}\:\mathrm{can}\:\mathrm{without}\:\mathrm{taking}\:\mathrm{the}\:\mathrm{same}\:\mathrm{3}\:\mathrm{children} \\ $$$$\mathrm{together}\:\mathrm{more}\:\mathrm{than}\:\mathrm{once}.\:\mathrm{The}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{times}\:\mathrm{each}\:\mathrm{child}\:\mathrm{will}\:\mathrm{go}\:\mathrm{to}\:\mathrm{the}\:\mathrm{garden} \\ $$$$\mathrm{is} \\ $$

Question Number 94632 Answers: 0 Comments: 1

The coefficient of x^m and x^n (m, n ∈ N) in the expansion of (1+x)^(m+n) are

$$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{{m}} \:\mathrm{and}\:{x}^{{n}} \left({m},\:{n}\:\in\:{N}\right)\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+{x}\right)^{{m}+{n}} \:\mathrm{are} \\ $$

Question Number 94629 Answers: 1 Comments: 0

In △ABC, a=(√3)+1, B=30°, C=45°, then c = ____.

$$\mathrm{In}\:\bigtriangleup{ABC},\:{a}=\sqrt{\mathrm{3}}+\mathrm{1},\:{B}=\mathrm{30}°,\:{C}=\mathrm{45}°, \\ $$$$\mathrm{then}\:{c}\:=\:\_\_\_\_. \\ $$

Question Number 94628 Answers: 1 Comments: 0

The perimeter of a △ ABC is 6 times the arithmetic mean of the sines of its angles. If the side a is 1, then the angle A is

$$\mathrm{The}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{a}\:\bigtriangleup\:{ABC}\:\mathrm{is}\:\mathrm{6}\:\mathrm{times} \\ $$$$\mathrm{the}\:\mathrm{arithmetic}\:\mathrm{mean}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sines}\:\mathrm{of} \\ $$$$\mathrm{its}\:\mathrm{angles}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{side}\:{a}\:\mathrm{is}\:\:\mathrm{1},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{angle}\:{A}\:\:\mathrm{is} \\ $$

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