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Question Number 157231 Answers: 2 Comments: 0

SOLVE : ⌊ x ⌋ + ⌊2x ⌋ +⌊ 3x ⌋= 1 −−−−−−−−−−

$$ \\ $$$$\:\:\:\:\:\:\mathcal{SOLVE}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\lfloor\:{x}\:\rfloor\:+\:\lfloor\mathrm{2}{x}\:\rfloor\:+\lfloor\:\mathrm{3}{x}\:\rfloor=\:\mathrm{1} \\ $$$$−−−−−−−−−− \\ $$$$ \\ $$

Question Number 157433 Answers: 0 Comments: 0

Question Number 157230 Answers: 1 Comments: 0

(3x+1)^(100) Find this max Koeffitcient

$$\left(\mathrm{3x}+\mathrm{1}\right)^{\mathrm{100}} \:\: \\ $$$$\mathrm{Find}\:\mathrm{this}\:\mathrm{max}\:\mathrm{Koeffitcient} \\ $$

Question Number 157438 Answers: 1 Comments: 0

find all subgroups of : a) grup (Z_6 , +) b) grup (Z_6 −{0}, ×)

$$\mathrm{find}\:\mathrm{all}\:\mathrm{subgroups}\:\mathrm{of}\:: \\ $$$$\left.\mathrm{a}\right)\:\mathrm{grup}\:\left(\mathrm{Z}_{\mathrm{6}} \:,\:+\right) \\ $$$$\left.\mathrm{b}\right)\:\mathrm{grup}\:\left(\mathrm{Z}_{\mathrm{6}} \:−\left\{\mathrm{0}\right\},\:×\right) \\ $$

Question Number 157436 Answers: 1 Comments: 0

if x;y;z≥0 then: 2^(x+y+z) + 2 ≥ 2^x + 2^y + 2^z

$$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\geqslant\mathrm{0}\:\:\mathrm{then}: \\ $$$$\mathrm{2}^{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}} \:+\:\mathrm{2}\:\geqslant\:\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{y}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{z}}} \\ $$$$ \\ $$

Question Number 157435 Answers: 1 Comments: 0

Question Number 157225 Answers: 0 Comments: 2

Question Number 157219 Answers: 0 Comments: 0

Σ_(0<n) (((−1)^(n−1) n)/(sinh(πn)))=(1/(4π)) prove

$$\underset{\mathrm{0}<\boldsymbol{\mathrm{n}}} {\sum}\frac{\left(−\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}−\mathrm{1}} \boldsymbol{\mathrm{n}}}{\boldsymbol{\mathrm{sinh}}\left(\pi\boldsymbol{\mathrm{n}}\right)}=\frac{\mathrm{1}}{\mathrm{4}\pi}\:\:\:\:{prove} \\ $$

Question Number 157254 Answers: 1 Comments: 0

Show that ∫_0 ^1 (1/((x+1)(x+2)))dx = ln((4/3))

$$\mathrm{Show}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}{dx}\:=\:\mathrm{ln}\left(\frac{\mathrm{4}}{\mathrm{3}}\right) \\ $$

Question Number 157199 Answers: 1 Comments: 0

What is the general expression of the divergence(divV^⇢ )

$${What}\:{is}\:{the}\:{general}\:{expression}\:{of}\:{the}\:{divergence}\left({div}\overset{\dashrightarrow} {{V}}\right) \\ $$

Question Number 157227 Answers: 1 Comments: 0

x(3sin((√x))−2(√x))=sin^3 ((√x))

$$\boldsymbol{\mathrm{x}}\left(\mathrm{3}\boldsymbol{\mathrm{sin}}\left(\sqrt{\boldsymbol{\mathrm{x}}}\right)−\mathrm{2}\sqrt{\boldsymbol{\mathrm{x}}}\right)=\boldsymbol{\mathrm{sin}}^{\mathrm{3}} \left(\sqrt{\boldsymbol{\mathrm{x}}}\right) \\ $$

Question Number 157191 Answers: 1 Comments: 0

lim_(x→0) ((sin x − x + (1/6) x^3 )/x^5 ) = ? ( Without L′Hospital , Taylor or Maclaurin Series ) .

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{sin}\:{x}\:−\:{x}\:+\:\frac{\mathrm{1}}{\mathrm{6}}\:{x}^{\mathrm{3}} }{{x}^{\mathrm{5}} }\:\:\:=\:\:? \\ $$$$\left(\:{Without}\:\:{L}'{Hospital}\:,\:{Taylor}\:\:{or}\:\:{Maclaurin}\:\:{Series}\:\right)\:. \\ $$

Question Number 157184 Answers: 1 Comments: 0

p(x)=x^3 −3ax^2 +(3a^2 +1)x−(a^3 +a) p(2)<0 prove that 2<a<3

$${p}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{3}{ax}^{\mathrm{2}} +\left(\mathrm{3}{a}^{\mathrm{2}} +\mathrm{1}\right){x}−\left({a}^{\mathrm{3}} +{a}\right) \\ $$$${p}\left(\mathrm{2}\right)<\mathrm{0} \\ $$$${prove}\:{that}\:\mathrm{2}<{a}<\mathrm{3} \\ $$

Question Number 157220 Answers: 1 Comments: 0

x = (1/2) find (√(x + 1 + (√(x^2 + 1)))) = ?

$$\mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{find}\:\:\sqrt{\mathrm{x}\:+\:\mathrm{1}\:+\:\sqrt{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}}}\:=\:? \\ $$

Question Number 157177 Answers: 1 Comments: 0

Question Number 157217 Answers: 0 Comments: 2

show that ((cos2x+cos3x+cos8x)/(sin2x+sin3x+sin8x))=tanx

$${show}\:{that} \\ $$$$\:\frac{{cos}\mathrm{2}{x}+{cos}\mathrm{3}{x}+{cos}\mathrm{8}{x}}{{sin}\mathrm{2}{x}+{sin}\mathrm{3}{x}+{sin}\mathrm{8}{x}}={tanx} \\ $$

Question Number 157216 Answers: 1 Comments: 1

lim_(x→∞) (((n!)/n^n ))^(1/n) =? lim_(x→0) ((√(tan 4x))/(tan(√(4x))))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{n}!}{{n}^{{n}} }\right)^{\frac{\mathrm{1}}{{n}}} =? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{tan}\:\mathrm{4}{x}}}{\mathrm{tan}\sqrt{\mathrm{4}{x}}}=? \\ $$

Question Number 157222 Answers: 2 Comments: 0

Question Number 157223 Answers: 2 Comments: 0

Question Number 157175 Answers: 2 Comments: 1

Question Number 157171 Answers: 1 Comments: 0

calculate lim_(n→+∞) (((n+ln(n)+1)/((5+(√n))^2 )))

$${calculate}\:\underset{{n}\rightarrow+\infty} {{lim}}\left(\frac{{n}+{ln}\left({n}\right)+\mathrm{1}}{\left(\mathrm{5}+\sqrt{{n}}\right)^{\mathrm{2}} }\right) \\ $$

Question Number 157169 Answers: 1 Comments: 0

Question Number 157168 Answers: 1 Comments: 0

x , y and z are numbers. Show that max(x, y)=((x+y+∣x−y∣)/2) and min(x,y)=((x+y−∣x−y∣)/2) then find a formula for max(x,y,z).

$${x}\:,\:{y}\:{and}\:{z}\:{are}\:{numbers}. \\ $$$${Show}\:{that}\:{max}\left({x},\:{y}\right)=\frac{{x}+{y}+\mid{x}−{y}\mid}{\mathrm{2}}\:{and}\:{min}\left({x},{y}\right)=\frac{{x}+{y}−\mid{x}−{y}\mid}{\mathrm{2}} \\ $$$${then}\:{find}\:{a}\:{formula}\:{for}\: \\ $$$${max}\left({x},{y},{z}\right). \\ $$

Question Number 157156 Answers: 1 Comments: 0

{ ((a_1 =((√3)/2))),((a_(n+1) =4a_n ^3 −3a_n ; ∀n≥1)) :} a_n =?

$$ \\ $$$$\:\begin{cases}{{a}_{\mathrm{1}} =\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}\\{{a}_{{n}+\mathrm{1}} =\mathrm{4}{a}_{{n}} ^{\mathrm{3}} −\mathrm{3}{a}_{{n}} \:;\:\forall{n}\geqslant\mathrm{1}}\end{cases} \\ $$$$\:{a}_{{n}} =? \\ $$

Question Number 157163 Answers: 1 Comments: 1

Find the positive integer solution of the equation: x^3 + y^3 = 7∙(14xy + 3)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{solution} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:=\:\mathrm{7}\centerdot\left(\mathrm{14xy}\:+\:\mathrm{3}\right) \\ $$

Question Number 157150 Answers: 0 Comments: 0

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