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Question Number 141492    Answers: 0   Comments: 1

Question Number 141437    Answers: 0   Comments: 0

Question Number 141435    Answers: 1   Comments: 0

Find all the arraangment of all the letters of the word SYLLABUSES such that each word contains the word BUS.

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{arraangment}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{letters} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\mathrm{SYLLABUSES}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{each}\:\mathrm{word}\:\mathrm{contains}\:\mathrm{the}\:\mathrm{word}\:\mathrm{BUS}. \\ $$

Question Number 141431    Answers: 2   Comments: 0

2∫_0 ^( 1) ∫_0 ^( 2) (x+2y)^8 dxdy

$$\mathrm{2}\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{2}} \left({x}+\mathrm{2}{y}\right)^{\mathrm{8}} \:{dxdy} \\ $$

Question Number 141419    Answers: 2   Comments: 0

𝛗:=∫_0 ^( ∞) ((ln(cosh(x)))/(cosh(x)))dx=^? ∫_0 ^( (Ο€/2)) log((1/(sin(x))))dx

$$ \\ $$$$\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left({cosh}\left({x}\right)\right)}{{cosh}\left({x}\right)}{dx}\overset{?} {=}\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {log}\left(\frac{\mathrm{1}}{{sin}\left({x}\right)}\right){dx} \\ $$

Question Number 141409    Answers: 1   Comments: 0

Prove that βˆ€n∈N ∫^( n+1) _n lnt dt ≀ ln(n+(1/2))

$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\forall\mathrm{n}\in\mathbb{N}\:\:\:\:\underset{\mathrm{n}} {\int}^{\:\mathrm{n}+\mathrm{1}} \mathrm{lnt}\:\mathrm{dt}\:\leqslant\:\mathrm{ln}\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$

Question Number 141407    Answers: 2   Comments: 0

Ξ©:=∫_0 ^( ∞) (dx/((x^4 βˆ’x^2 +1)^3 ))=?

$$ \\ $$$$\:\:\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\infty} \frac{{dx}}{\left({x}^{\mathrm{4}} βˆ’{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }=? \\ $$

Question Number 141405    Answers: 1   Comments: 0

Find the minimum value of k such that for arbitrary a,b >0 we have (a)^(1/(3 )) + (b)^(1/(3 )) ≀ k ((a+b))^(1/(3 ))

$$\:\:\:\:\:{Find}\:{the}\:{minimum}\:{value}\:{of}\:{k} \\ $$$$\:\:\:\:\:{such}\:{that}\:{for}\:{arbitrary}\:{a},{b}\:>\mathrm{0} \\ $$$$\:\:\:\:\:{we}\:{have}\:\:\sqrt[{\mathrm{3}\:}]{{a}}\:+\:\sqrt[{\mathrm{3}\:}]{{b}}\:\leqslant\:{k}\:\sqrt[{\mathrm{3}\:}]{{a}+{b}}\: \\ $$

Question Number 141423    Answers: 1   Comments: 0

tan (x+y)= ((12)/5) sin (xβˆ’y) = (3/5) x+y , xβˆ’y are acute angles . tan x tan y = ?

$$\mathrm{tan}\:\left({x}+{y}\right)=\:\frac{\mathrm{12}}{\mathrm{5}} \\ $$$$\mathrm{sin}\:\left({x}βˆ’{y}\right)\:=\:\frac{\mathrm{3}}{\mathrm{5}} \\ $$$${x}+{y}\:,\:{x}βˆ’{y}\:\:{are}\:\:{acute}\:\:{angles}\:. \\ $$$$\mathrm{tan}\:{x}\:\mathrm{tan}\:{y}\:=\:\:? \\ $$

Question Number 141400    Answers: 3   Comments: 0

fjnd inverse of matrix [(2,(βˆ’5)),(1,3) ]

$${fjnd}\:{inverse}\:{of}\:{matrix}\begin{bmatrix}{\mathrm{2}}&{βˆ’\mathrm{5}}\\{\mathrm{1}}&{\mathrm{3}}\end{bmatrix} \\ $$

Question Number 141398    Answers: 0   Comments: 0

Question Number 141395    Answers: 1   Comments: 0

A 64.00 cm3 piece of wood is in the shape of a cube. A lazy ant wants to walk from one corner to the very opposite corner of the cube. What is its minimum path length?

$$ \\ $$A 64.00 cm3 piece of wood is in the shape of a cube. A lazy ant wants to walk from one corner to the very opposite corner of the cube. What is its minimum path length?

Question Number 141365    Answers: 1   Comments: 0

log _(9/4) ((1/(2(√3)))(√(6βˆ’(1/(2(√3)))(√(6βˆ’(1/(2(√3)))(√(6βˆ’(1/(2(√3)))(√(...))))))))) =?

$$\:\mathrm{log}\:_{\frac{\mathrm{9}}{\mathrm{4}}} \left(\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}βˆ’\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}βˆ’\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}βˆ’\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{...}}}}\right)\:=? \\ $$

Question Number 141360    Answers: 0   Comments: 1

∫_0 ^(Ο€/2) (√(cosxsenx))dx

$$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \sqrt{{cosxsenx}}{dx} \\ $$

Question Number 141359    Answers: 0   Comments: 2

Question Number 141356    Answers: 2   Comments: 0

lim_(xβ†’+∞) (((x+1)/( (√(x^2 +1)))) βˆ’1)

$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{{x}+\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:βˆ’\mathrm{1}\right) \\ $$

Question Number 141362    Answers: 1   Comments: 0

∫sen(2θ)cos^4 (2θ)dθ

$$\int{sen}\left(\mathrm{2}\theta\right){cos}^{\mathrm{4}} \left(\mathrm{2}\theta\right){d}\theta \\ $$

Question Number 141352    Answers: 1   Comments: 0

Question Number 141346    Answers: 1   Comments: 0

Question Number 141345    Answers: 0   Comments: 0

((log(ΞΆ(s)))/s)=∫_1 ^∞ J(x)x^(βˆ’sβˆ’1) dx ( Prove that) Here J(x)=Ο€(x)+(1/2)Ο€((√x))+(1/3)Ο€((x)^(1/3) )+... Ο€(x):=Prime counting function

$$\frac{{log}\left(\zeta\left({s}\right)\right)}{{s}}=\int_{\mathrm{1}} ^{\infty} {J}\left({x}\right){x}^{βˆ’{s}βˆ’\mathrm{1}} {dx}\:\left(\:{Prove}\:{that}\right) \\ $$$${Here}\:\:{J}\left({x}\right)=\pi\left({x}\right)+\frac{\mathrm{1}}{\mathrm{2}}\pi\left(\sqrt{{x}}\right)+\frac{\mathrm{1}}{\mathrm{3}}\pi\left(\sqrt[{\mathrm{3}}]{{x}}\right)+... \\ $$$$\pi\left({x}\right):=\boldsymbol{\mathrm{P}{rime}}\:\boldsymbol{{counting}}\:\boldsymbol{{function}} \\ $$

Question Number 141340    Answers: 0   Comments: 0

Given the function f defined by f(x) = { ((((2e^x )/(e^x βˆ’1)),xβ‰  0)),((0, x = 0)) :} (i) study the differentiability of f at x = 0. (ii) Show that the point (0,1) is the centre of symetry to the curve of f.

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{function}\:{f}\:\mathrm{defined}\:\mathrm{by} \\ $$$$\:{f}\left({x}\right)\:=\:\begin{cases}{\frac{\mathrm{2}{e}^{{x}} }{{e}^{{x}} βˆ’\mathrm{1}},{x}\neq\:\mathrm{0}}\\{\mathrm{0},\:{x}\:=\:\mathrm{0}}\end{cases} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{study}\:\mathrm{the}\:\mathrm{differentiability}\:\mathrm{of}\:{f}\:\mathrm{at}\:{x}\:=\:\mathrm{0}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{0},\mathrm{1}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{symetry}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{curve}\:\mathrm{of}\:{f}. \\ $$

Question Number 141336    Answers: 2   Comments: 0

∫sin (ln (x))dx=? Please

$$\int\mathrm{sin}\:\left(\mathrm{ln}\:\left({x}\right)\right){dx}=?\:\:{Please} \\ $$

Question Number 141417    Answers: 2   Comments: 0

........ advanced ... ... ... calculus....... prove that:: F:= ∫_(βˆ’1) ^( 0) ((e^x +e^(1/x) βˆ’1)/x) dx=^(??) Ξ³

$$\:\:\:\:\:\:\:\:\:\:........\:{advanced}\:...\:...\:...\:{calculus}....... \\ $$$$\:\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:\:\mathscr{F}:=\:\int_{βˆ’\mathrm{1}} ^{\:\mathrm{0}} \frac{{e}^{{x}} +{e}^{\frac{\mathrm{1}}{{x}}} βˆ’\mathrm{1}}{{x}}\:{dx}\overset{??} {=}\gamma \\ $$

Question Number 141414    Answers: 0   Comments: 1

Question Number 141413    Answers: 1   Comments: 0

∫^( +∞) _( 1) ((1/(E(x)))βˆ’(1/x))dx=???

$$\underset{\:\mathrm{1}} {\int}^{\:+\infty} \left(\frac{\mathrm{1}}{\mathrm{E}\left(\mathrm{x}\right)}βˆ’\frac{\mathrm{1}}{\mathrm{x}}\right)\mathrm{dx}=??? \\ $$

Question Number 141333    Answers: 1   Comments: 0

∫x^2 cos ((x/2))dx

$$\int{x}^{\mathrm{2}} \mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right){dx} \\ $$

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