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Question Number 149234 Answers: 1 Comments: 0

(x/2) + log_2 (x + 12) = 6 ⇒ x = ?

$$\frac{{x}}{\mathrm{2}}\:+\:{log}_{\mathrm{2}} \left({x}\:+\:\mathrm{12}\right)\:=\:\mathrm{6} \\ $$$$\Rightarrow\:\boldsymbol{{x}}\:=\:? \\ $$

Question Number 149233 Answers: 0 Comments: 0

Question Number 149219 Answers: 2 Comments: 0

Question Number 149212 Answers: 1 Comments: 0

if x;y;z>0 and xyz=1 prove that: (x^4 /(x+yz)) + (y^4 /(y+zx)) + (z^4 /(z+xy)) ≥ (3/2)

$${if}\:\:\:{x};{y};{z}>\mathrm{0}\:\:\:{and}\:\:\:{xyz}=\mathrm{1}\:\:\:{prove}\:{that}: \\ $$$$\frac{{x}^{\mathrm{4}} }{{x}+{yz}}\:+\:\frac{{y}^{\mathrm{4}} }{{y}+{zx}}\:+\:\frac{{z}^{\mathrm{4}} }{{z}+{xy}}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$

Question Number 149192 Answers: 1 Comments: 0

Question Number 149191 Answers: 2 Comments: 0

......calculus..... ∫_0 ^( ∞) ((sech(πx))/(1+4x^( 2) )) dx=? .........m.n...

$$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:......{calculus}..... \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sech}\left(\pi{x}\right)}{\mathrm{1}+\mathrm{4}{x}^{\:\mathrm{2}} }\:{dx}=? \\ $$$$\:.........{m}.{n}... \\ $$

Question Number 149189 Answers: 2 Comments: 1

Question Number 149188 Answers: 2 Comments: 0

f(x) = ax^(99) + bx^(77) + cx^(55) + 975 f(−975) = 1000 find f(975) = ?

$${f}\left({x}\right)\:=\:{ax}^{\mathrm{99}} \:+\:{bx}^{\mathrm{77}} \:+\:{cx}^{\mathrm{55}} \:+\:\mathrm{975} \\ $$$${f}\left(−\mathrm{975}\right)\:=\:\mathrm{1000} \\ $$$${find}\:\:\:{f}\left(\mathrm{975}\right)\:=\:? \\ $$

Question Number 149187 Answers: 0 Comments: 2

Question Number 149186 Answers: 0 Comments: 0

Question Number 149184 Answers: 1 Comments: 0

Ω =lim_(x→1) ((tan (√(3x+2))−tan (√(2x+3)))/(tan (√(5x+4))−tan (√(4x+5)))) =?

$$\:\:\:\Omega\:=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{tan}\:\sqrt{\mathrm{3x}+\mathrm{2}}−\mathrm{tan}\:\sqrt{\mathrm{2x}+\mathrm{3}}}{\mathrm{tan}\:\sqrt{\mathrm{5x}+\mathrm{4}}−\mathrm{tan}\:\sqrt{\mathrm{4x}+\mathrm{5}}}\:=? \\ $$

Question Number 149180 Answers: 1 Comments: 0

Question Number 149205 Answers: 1 Comments: 0

∫_(−∞) ^0 (t/((1−t)^2 ))dt

$$\int_{−\infty} ^{\mathrm{0}} \frac{{t}}{\left(\mathrm{1}−{t}\right)^{\mathrm{2}} }{dt} \\ $$

Question Number 149204 Answers: 0 Comments: 0

Question Number 149208 Answers: 1 Comments: 0

If loga and logb are the roots of the equation mx^2 +nx+s=0, fimd in terms of m, n and s the value of logab.

$$\mathrm{If}\:\mathrm{loga}\:\mathrm{and}\:\mathrm{logb}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{mx}^{\mathrm{2}} +\mathrm{nx}+\mathrm{s}=\mathrm{0},\:\mathrm{fimd}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{m},\:\mathrm{n}\:\mathrm{and} \\ $$$$\mathrm{s}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{logab}. \\ $$

Question Number 149171 Answers: 2 Comments: 0

2^(2x ) + 4^(3x) = 128 ⇒x=?

$$\:\mathrm{2}^{\mathrm{2x}\:} \:+\:\mathrm{4}^{\mathrm{3x}} \:=\:\mathrm{128}\:\Rightarrow\mathrm{x}=? \\ $$

Question Number 149163 Answers: 0 Comments: 0

Q[(√3)]/ker f define the circular element of the unit

$${Q}\left[\sqrt{\mathrm{3}}\right]/{ker}\:{f}\:\:{define}\:{the}\:{circular} \\ $$$${element}\:{of}\:{the}\:{unit} \\ $$

Question Number 149157 Answers: 1 Comments: 0

∫_(1/2) ^2 (1/x)cosec^(101) (x−(1/x)) dx=?

$$\underset{\frac{\mathrm{1}}{\mathrm{2}}} {\overset{\mathrm{2}} {\int}}\frac{\mathrm{1}}{{x}}\mathrm{cosec}\:^{\mathrm{101}} \left({x}−\frac{\mathrm{1}}{{x}}\right)\:{dx}=? \\ $$

Question Number 149156 Answers: 0 Comments: 0

if ∫(dx/( (((1+x^2 )^(1012) (2+x^2 )^(3012) ))^(1/(2012)) ))=(α/(2β))(1−f(x))^(β/α) then find α,β,f(x)

$${if}\:\int\frac{{dx}}{\:\sqrt[{\mathrm{2012}}]{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{1012}} \left(\mathrm{2}+{x}^{\mathrm{2}} \right)^{\mathrm{3012}} }}=\frac{\alpha}{\mathrm{2}\beta}\left(\mathrm{1}−{f}\left({x}\right)\right)^{\frac{\beta}{\alpha}} \\ $$$${then}\:{find}\:\alpha,\beta,{f}\left({x}\right) \\ $$

Question Number 149155 Answers: 0 Comments: 0

find the coefficient of x^(50) in the (1+x)^(1000) +2x(1+x)^(999) +3x^2 (1+x)^(998) +...∞

$${find}\:{the}\:{coefficient}\:{of}\:{x}^{\mathrm{50}} \:{in}\:{the}\: \\ $$$$\left(\mathrm{1}+{x}\right)^{\mathrm{1000}} +\mathrm{2}{x}\left(\mathrm{1}+{x}\right)^{\mathrm{999}} +\mathrm{3}{x}^{\mathrm{2}} \left(\mathrm{1}+{x}\right)^{\mathrm{998}} +...\infty\: \\ $$

Question Number 149151 Answers: 4 Comments: 0

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

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

Question Number 149150 Answers: 1 Comments: 0

∫ ln (cosx) dx = ?

$$\int\:{ln}\:\left({cosx}\right)\:{dx}\:=\:? \\ $$

Question Number 149142 Answers: 1 Comments: 0

if z + ∣z∣ = 1 + (√3) i find 𝛟 = ?

$${if}\:\:\:{z}\:+\:\mid{z}\mid\:=\:\mathrm{1}\:+\:\sqrt{\mathrm{3}}\:\boldsymbol{{i}} \\ $$$${find}\:\:\:\boldsymbol{\varphi}\:=\:? \\ $$

Question Number 149141 Answers: 0 Comments: 2

((cos^2 (70) - sin^2 (70))/(sin(100) + sin(20))) = ?

$$\frac{{cos}^{\mathrm{2}} \left(\mathrm{70}\right)\:-\:{sin}^{\mathrm{2}} \left(\mathrm{70}\right)}{{sin}\left(\mathrm{100}\right)\:+\:{sin}\left(\mathrm{20}\right)}\:=\:? \\ $$

Question Number 149140 Answers: 0 Comments: 2

{ ((∣x∣ + y - 1 = 0)),((x - y - 1 = 0)) :} ⇒ 2x - 3y = ?

$$\begin{cases}{\mid{x}\mid\:+\:{y}\:-\:\mathrm{1}\:=\:\mathrm{0}}\\{{x}\:-\:{y}\:-\:\mathrm{1}\:=\:\mathrm{0}}\end{cases}\:\:\:\Rightarrow\:\:\mathrm{2}{x}\:-\:\mathrm{3}{y}\:=\:? \\ $$

Question Number 149129 Answers: 2 Comments: 1

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