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AllQuestion and Answers: Page 995

Question Number 119930 Answers: 1 Comments: 0

Question Number 119928 Answers: 2 Comments: 0

Question Number 119922 Answers: 0 Comments: 0

Question Number 119921 Answers: 2 Comments: 0

solving the following system of equations { ((((3x−y)/(x−3y))=x^2 )),((((3y−z)/(y−3z))=y^2 )),((((3z−x)/(z−3x))=z^2 )) :}

$${solving}\:{the}\:{following}\:{system}\:{of}\:{equations} \\ $$$$\begin{cases}{\frac{\mathrm{3}{x}−{y}}{{x}−\mathrm{3}{y}}={x}^{\mathrm{2}} }\\{\frac{\mathrm{3}{y}−{z}}{{y}−\mathrm{3}{z}}={y}^{\mathrm{2}} }\\{\frac{\mathrm{3}{z}−{x}}{{z}−\mathrm{3}{x}}={z}^{\mathrm{2}} }\end{cases} \\ $$

Question Number 119920 Answers: 5 Comments: 0

∫ (√((1−x)/(1+x))) dx = ? , xε(−1,1)

$$\:\int\:\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\:{dx}\:=\:?\:,\:{x}\epsilon\left(−\mathrm{1},\mathrm{1}\right) \\ $$

Question Number 119919 Answers: 1 Comments: 0

sin 70° cos 50° + sin 260° cos 280° =?

$$\:\mathrm{sin}\:\mathrm{70}°\:\mathrm{cos}\:\mathrm{50}°\:+\:\mathrm{sin}\:\mathrm{260}°\:\mathrm{cos}\:\mathrm{280}°\:=? \\ $$

Question Number 119915 Answers: 1 Comments: 0

Question Number 119914 Answers: 0 Comments: 0

Question Number 119909 Answers: 2 Comments: 0

Given f(x)=((px+q)/(x+2)) , q≠ 0 f^(−1) (q) = −1 then f^(−1) (2q)=?

$${Given}\:{f}\left({x}\right)=\frac{{px}+{q}}{{x}+\mathrm{2}}\:,\:{q}\neq\:\mathrm{0} \\ $$$${f}^{−\mathrm{1}} \:\left({q}\right)\:=\:−\mathrm{1}\:{then}\:{f}^{−\mathrm{1}} \left(\mathrm{2}{q}\right)=? \\ $$

Question Number 119902 Answers: 3 Comments: 0

lim_(x→0) (cos x)^(1/(sin^2 x)) ?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{cos}\:{x}\right)^{\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} {x}}} \:? \\ $$

Question Number 119896 Answers: 2 Comments: 1

Question Number 119894 Answers: 2 Comments: 0

Question Number 119893 Answers: 2 Comments: 0

Question Number 119892 Answers: 1 Comments: 0

Question Number 119891 Answers: 0 Comments: 0

show that (d/dx) Γ(x)=∫_0 ^∞ t^(x−1) e^(−t) lnt dt

$${show}\:{that}\: \\ $$$$\frac{{d}}{{dx}}\:\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\infty} {t}^{{x}−\mathrm{1}} {e}^{−{t}} {lnt}\:{dt} \\ $$

Question Number 119876 Answers: 0 Comments: 0

Question Number 119875 Answers: 3 Comments: 1

Question Number 119866 Answers: 1 Comments: 4

Question Number 119867 Answers: 1 Comments: 2

lim_(x→∞) (((1+(1/(2n)))^n −(√e))/((1+(2/n))^n −e^2 ))=???

$${li}\underset{{x}\rightarrow\infty} {{m}}\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}{n}}\right)^{{n}} −\sqrt{{e}}}{\left(\mathrm{1}+\frac{\mathrm{2}}{{n}}\right)^{{n}} −{e}^{\mathrm{2}} }=??? \\ $$

Question Number 119856 Answers: 0 Comments: 4

i have forgotten my password. how may i retrieve it? please help me or forward me to one of the developers please

$$\mathrm{i}\:\mathrm{have}\:\mathrm{forgotten}\:\mathrm{my}\:\mathrm{password}. \\ $$$$\mathrm{how}\:\mathrm{may}\:\mathrm{i}\:\mathrm{retrieve}\:\mathrm{it}? \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{or}\:\mathrm{forward}\:\mathrm{me}\:\mathrm{to} \\ $$$$\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{developers}\:\mathrm{please} \\ $$

Question Number 119852 Answers: 1 Comments: 0

lim_(n→∞) n^2 ∫ _0 ^(1/n) x^(x+1) dx =?

$$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}^{\mathrm{2}} \:\int\:\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{{n}}} {\:}}{x}^{{x}+\mathrm{1}} \:{dx}\:=? \\ $$

Question Number 119849 Answers: 1 Comments: 0

Find all pair(x,y) of real numbers that are the solutions to the system { ((x^4 +2x^3 −y=−(1/4)+(√3))),((y^4 +2y^3 −x=−(1/4)−(√3))) :}

$${Find}\:{all}\:{pair}\left({x},{y}\right)\:{of}\:{real}\:{numbers} \\ $$$${that}\:{are}\:{the}\:{solutions}\:{to}\:{the}\:{system} \\ $$$$\begin{cases}{{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}} −{y}=−\frac{\mathrm{1}}{\mathrm{4}}+\sqrt{\mathrm{3}}}\\{{y}^{\mathrm{4}} +\mathrm{2}{y}^{\mathrm{3}} −{x}=−\frac{\mathrm{1}}{\mathrm{4}}−\sqrt{\mathrm{3}}}\end{cases} \\ $$

Question Number 119848 Answers: 1 Comments: 0

Solve in real numbers the equation (x)^(1/(3 )) + ((x−1))^(1/(3 )) + ((x+1))^(1/(3 )) = 0

$${Solve}\:{in}\:{real}\:{numbers}\:{the}\:{equation} \\ $$$$\sqrt[{\mathrm{3}\:}]{{x}}\:+\:\sqrt[{\mathrm{3}\:}]{{x}−\mathrm{1}}\:+\:\sqrt[{\mathrm{3}\:}]{{x}+\mathrm{1}}\:=\:\mathrm{0} \\ $$

Question Number 119839 Answers: 1 Comments: 0

Prove that sin x−cos^2 x+sin^3 x−cos^4 x+sin^5 x−cos^6 x +sin^7 x−cos^8 x+……=(√2)−1

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{sin}\:{x}−\mathrm{cos}^{\mathrm{2}} {x}+\mathrm{sin}^{\mathrm{3}} {x}−\mathrm{cos}^{\mathrm{4}} {x}+\mathrm{sin}^{\mathrm{5}} {x}−\mathrm{cos}^{\mathrm{6}} {x} \\ $$$$+\mathrm{sin}^{\mathrm{7}} {x}−\mathrm{cos}^{\mathrm{8}} {x}+\ldots\ldots=\sqrt{\mathrm{2}}−\mathrm{1} \\ $$

Question Number 119837 Answers: 0 Comments: 0

find lim_(n→+∞) ∫_0 ^(√n) (1−(x/(√n)))^(√(2n)) arctan(((πx)/n))dx

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

Question Number 119835 Answers: 2 Comments: 1

If M and m are respectively the largest and the smallest integers that satisfying the inequality 6n^2 −5n≤99, find the value of M−m.

$$\mathrm{If}\:{M}\:\mathrm{and}\:{m}\:\mathrm{are}\:\mathrm{respectively}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{smallest}\:\mathrm{integers}\:\mathrm{that}\:\mathrm{satisfying}\:\mathrm{the} \\ $$$$\mathrm{inequality}\:\mathrm{6}{n}^{\mathrm{2}} −\mathrm{5}{n}\leqslant\mathrm{99},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${M}−{m}. \\ $$

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