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Question Number 181875 Answers: 4 Comments: 3

if a+b+c=0, find the maximum of ((∣a+2b+3c∣)/( (√(a^2 +b^2 +c^2 )))).

$${if}\:{a}+{b}+{c}=\mathrm{0},\:{find}\:{the}\:{maximum}\:{of} \\ $$$$\frac{\mid{a}+\mathrm{2}{b}+\mathrm{3}{c}\mid}{\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }}. \\ $$

Question Number 181872 Answers: 1 Comments: 0

∫_(−1) ^4 (1/(∣x∣)) dx

$$\underset{−\mathrm{1}} {\overset{\mathrm{4}} {\int}}\frac{\mathrm{1}}{\mid{x}\mid}\:{dx} \\ $$

Question Number 181869 Answers: 0 Comments: 1

Question Number 181863 Answers: 0 Comments: 0

cos 56°. cos (2.56°). cos (2^2 .56°). cos (2^3 .56°)... cos (2^(23) .56°)=?

$$\:\mathrm{cos}\:\mathrm{56}°.\:\mathrm{cos}\:\left(\mathrm{2}.\mathrm{56}°\right).\:\mathrm{cos}\:\left(\mathrm{2}^{\mathrm{2}} .\mathrm{56}°\right).\:\mathrm{cos}\:\left(\mathrm{2}^{\mathrm{3}} .\mathrm{56}°\right)...\:\mathrm{cos}\:\left(\mathrm{2}^{\mathrm{23}} .\mathrm{56}°\right)=? \\ $$

Question Number 181858 Answers: 2 Comments: 0

Question Number 181857 Answers: 1 Comments: 0

Question Number 181853 Answers: 0 Comments: 3

∫ cos^(−1) (tan^3 (tan(x))) dx= ?

$$\: \\ $$$$\int\:\boldsymbol{\mathrm{cos}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{tan}}^{\mathrm{3}} \left(\boldsymbol{\mathrm{tan}}\left(\boldsymbol{\mathrm{x}}\right)\right)\right)\:\boldsymbol{\mathrm{dx}}=\:? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 181852 Answers: 2 Comments: 0

Question Number 181851 Answers: 0 Comments: 0

∫ arccos(tg^3 (tg(x))) dx=?

$$\:\:\:\int\:\boldsymbol{\mathrm{arccos}}\left(\boldsymbol{\mathrm{tg}}^{\mathrm{3}} \left(\boldsymbol{\mathrm{tg}}\left(\boldsymbol{\mathrm{x}}\right)\right)\right)\:\boldsymbol{\mathrm{dx}}=? \\ $$

Question Number 181841 Answers: 3 Comments: 0

what is larger, (√(11))+(√(13)) or 7?

$${what}\:{is}\:{larger},\:\sqrt{\mathrm{11}}+\sqrt{\mathrm{13}}\:{or}\:\mathrm{7}? \\ $$

Question Number 181840 Answers: 0 Comments: 3

∫_(−1) ^4 ln x dx

$$\underset{−\mathrm{1}} {\overset{\mathrm{4}} {\int}}{ln}\:{x}\:{dx} \\ $$

Question Number 181839 Answers: 1 Comments: 5

Question Number 181836 Answers: 0 Comments: 0

∫_0 ^( 1) ∫_0 ^( 1) ((cos^(−1) (xy)sin^(−1) (xy))/(ln(xy)))dxdy

$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{cos}^{−\mathrm{1}} \left({xy}\right){sin}^{−\mathrm{1}} \left({xy}\right)}{{ln}\left({xy}\right)}{dxdy} \\ $$

Question Number 181832 Answers: 2 Comments: 1

help ! ∫ ((ln(x+1))/(x^2 +1))dx = ???

$$\mathrm{help}\:! \\ $$$$\int\:\frac{{ln}\left({x}+\mathrm{1}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}{dx}\:=\:??? \\ $$

Question Number 181837 Answers: 3 Comments: 2

find integers a>b>c>0 such that (1/a)+(2/b)+(3/c)=1

$${find}\:{integers}\:{a}>{b}>{c}>\mathrm{0}\:{such}\:{that} \\ $$$$\frac{\mathrm{1}}{{a}}+\frac{\mathrm{2}}{{b}}+\frac{\mathrm{3}}{{c}}=\mathrm{1} \\ $$

Question Number 181812 Answers: 5 Comments: 0

Question Number 181808 Answers: 3 Comments: 1

Question Number 181799 Answers: 1 Comments: 0

solve the difgerential equation y(√(1+(y′)^2 ))=y′

$$\:\boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{difgerential}}\:\boldsymbol{{equation}} \\ $$$$\boldsymbol{{y}}\sqrt{\mathrm{1}+\left(\boldsymbol{{y}}'\right)^{\mathrm{2}} }=\boldsymbol{{y}}'\: \\ $$

Question Number 181795 Answers: 0 Comments: 0

use laplace transform to slove y′′+4y=5u(t−1),y(0)=0,y′(0)=0

$${use}\:{laplace}\:{transform}\:{to}\:{slove}\: \\ $$$${y}''+\mathrm{4}{y}=\mathrm{5}{u}\left({t}−\mathrm{1}\right),{y}\left(\mathrm{0}\right)=\mathrm{0},{y}'\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$ \\ $$

Question Number 181794 Answers: 1 Comments: 0

f(0) = 0 f(1) = e^3 f ∈ C^2 (R) f^(′′) (x) − 5 f^′ (x) + 6 f(x) = 0 , ∀ x ∈ R Find: 𝛀 =lim_(x→∞) (1 − (1/(f (x))))^x

$$\mathrm{f}\left(\mathrm{0}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{f}\left(\mathrm{1}\right)\:=\:\mathrm{e}^{\mathrm{3}} \\ $$$$\mathrm{f}\:\in\:\mathbb{C}^{\mathrm{2}} \:\left(\mathbb{R}\right) \\ $$$$\mathrm{f}\:^{''} \:\left(\mathrm{x}\right)\:−\:\mathrm{5}\:\mathrm{f}\:^{'} \left(\mathrm{x}\right)\:+\:\mathrm{6}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{0}\:\:,\:\:\forall\:\mathrm{x}\:\in\:\mathbb{R} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\Omega}\:=\underset{\boldsymbol{\mathrm{x}}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{f}\:\left(\mathrm{x}\right)}\right)^{\boldsymbol{\mathrm{x}}} \\ $$

Question Number 181793 Answers: 0 Comments: 1

Please Calculate this problem ∫_0 ^1 dx ∫_x^2 ^(√x) dy=....

$$\mathrm{Please}\:\mathrm{Calculate}\:\mathrm{this}\:\mathrm{problem} \\ $$$$\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{dx}\:\underset{\mathrm{x}^{\mathrm{2}} } {\overset{\sqrt{\mathrm{x}}} {\int}}\:\mathrm{dy}=.... \\ $$

Question Number 181792 Answers: 0 Comments: 1

Please Calculate this integration 2∫_0 ^1 dx ∫_(2x) ^((2x)^(1/3) ) dy

$$\mathrm{Please}\:\mathrm{Calculate}\:\mathrm{this}\:\mathrm{integration} \\ $$$$\mathrm{2}\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{dx}\:\underset{\mathrm{2x}} {\overset{\left(\mathrm{2x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} } {\int}}\:\mathrm{dy} \\ $$

Question Number 181785 Answers: 0 Comments: 2

Question Number 181784 Answers: 0 Comments: 0

s_n =Σ_(k=n+1) ^(+oo) (1/k)=ln2 Σ_(k=1) ^(+oo) (((−1)^(k−1) )/k)=?

$${s}_{{n}} =\underset{{k}={n}+\mathrm{1}} {\overset{+{oo}} {\sum}}\frac{\mathrm{1}}{{k}}={ln}\mathrm{2} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{+{oo}} {\sum}}\frac{\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} }{{k}}=? \\ $$

Question Number 181783 Answers: 2 Comments: 0

one side of a triangle is 20 cm. the other two sides are in ratio 1:3. 1) what is the maximum area of the triangle, if exists? 2) what is the maximun perimeter of the triangle, if exists?

$${one}\:{side}\:{of}\:{a}\:{triangle}\:{is}\:\mathrm{20}\:{cm}.\:{the} \\ $$$${other}\:{two}\:{sides}\:{are}\:{in}\:{ratio}\:\mathrm{1}:\mathrm{3}. \\ $$$$\left.\mathrm{1}\right)\:{what}\:{is}\:{the}\:{maximum}\:{area}\:{of}\:{the} \\ $$$${triangle},\:{if}\:{exists}? \\ $$$$\left.\mathrm{2}\right)\:{what}\:{is}\:{the}\:{maximun}\:{perimeter} \\ $$$${of}\:{the}\:{triangle},\:{if}\:{exists}? \\ $$

Question Number 181779 Answers: 1 Comments: 0

3^(4x−11) +3^(10−x^2 ) +3^((x−2)^2 ) =6x−x^2

$$\mathrm{3}^{\mathrm{4x}−\mathrm{11}} +\mathrm{3}^{\mathrm{10}−\mathrm{x}^{\mathrm{2}} } +\mathrm{3}^{\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} } =\mathrm{6x}−\mathrm{x}^{\mathrm{2}} \\ $$

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