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AllQuestion and Answers: Page 1290

Question Number 84913 Answers: 2 Comments: 2

sin(π/(14)) sin((3π)/(14)) sin((5π)/(15))=?

$$ \\ $$$${sin}\frac{\pi}{\mathrm{14}}\:{sin}\frac{\mathrm{3}\pi}{\mathrm{14}}\:{sin}\frac{\mathrm{5}\pi}{\mathrm{15}}=? \\ $$

Question Number 84909 Answers: 2 Comments: 5

Find all solutions of (x, y) such that x^3 − 3xy^2 = 2010 y^3 − 3x^2 y = 2009 x, y ∈ R

$${Find}\:\:\:{all}\:\:{solutions}\:\:{of}\:\:\left({x},\:{y}\right)\:\:{such}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\:{x}^{\mathrm{3}} \:−\:\mathrm{3}{xy}^{\mathrm{2}} \:\:=\:\:\mathrm{2010} \\ $$$$\:\:\:\:\:\:\:\:{y}^{\mathrm{3}} \:−\:\mathrm{3}{x}^{\mathrm{2}} {y}\:\:=\:\:\mathrm{2009} \\ $$$${x},\:{y}\:\:\in\:\:\mathbb{R} \\ $$

Question Number 84904 Answers: 0 Comments: 1

3^(2x^2 ) + 3^(x^2 +2x+5) ≥ 10. 3^(4x+6)

$$\mathrm{3}^{\mathrm{2x}^{\mathrm{2}} } \:+\:\mathrm{3}^{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{5}} \:\geqslant\:\mathrm{10}.\:\mathrm{3}^{\mathrm{4x}+\mathrm{6}} \\ $$$$ \\ $$

Question Number 84902 Answers: 0 Comments: 2

lim_(x→∞) (5^x +5^(2x) )^(1/x) ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{5}^{\mathrm{x}} +\mathrm{5}^{\mathrm{2x}} \right)\:^{\frac{\mathrm{1}}{\mathrm{x}}} \:? \\ $$

Question Number 84899 Answers: 0 Comments: 1

Question Number 84894 Answers: 0 Comments: 1

Question Number 84892 Answers: 1 Comments: 4

Question Number 84891 Answers: 0 Comments: 0

Question Number 84890 Answers: 0 Comments: 3

If we have : y = e^x What is : (d/dy)e^x = ... If we derivate with y... Please...

$$\mathrm{If}\:\mathrm{we}\:\mathrm{have}\::\:\:\:\:\:{y}\:=\:{e}^{{x}} \\ $$$$ \\ $$$${W}\mathrm{hat}\:\mathrm{is}\::\:\:\:\frac{\mathrm{d}}{\mathrm{d}{y}}{e}^{{x}} \:=\:... \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{we}\:\mathrm{derivate}\:\mathrm{with}\:{y}... \\ $$$$ \\ $$$$\mathrm{Please}... \\ $$

Question Number 84884 Answers: 2 Comments: 1

Question Number 84879 Answers: 2 Comments: 1

e^(∫((2dx)/(xlnx)))

$$\mathrm{e}^{\int\frac{\mathrm{2dx}}{\mathrm{xlnx}}} \\ $$

Question Number 84873 Answers: 2 Comments: 1

lim_(x→∞) ((x^2 sin (((x!)/x)))/(x^2 +1))

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

Question Number 84871 Answers: 1 Comments: 1

If you know (((b^2 +c^2 −a^2 )/(2bc)))^2 +(((c^2 +a^2 −b^2 )/(2ca)))^2 +(((a^2 +b^2 −c^2 )/(2ab)))^2 =3, then what′s the value of ((b^2 +c^2 −a^2 )/(2bc))+((c^2 +a^2 −b^2 )/(2ac))+((a^2 +b^2 −c^2 )/(2ab))?

$$\mathrm{If}\:\mathrm{you}\:\mathrm{know} \\ $$$$\left(\frac{{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{2}{bc}}\right)^{\mathrm{2}} +\left(\frac{{c}^{\mathrm{2}} +{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{\mathrm{2}{ca}}\right)^{\mathrm{2}} +\left(\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{c}^{\mathrm{2}} }{\mathrm{2}{ab}}\right)^{\mathrm{2}} =\mathrm{3}, \\ $$$$\mathrm{then}\:\mathrm{what}'\mathrm{s}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{2}{bc}}+\frac{{c}^{\mathrm{2}} +{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{\mathrm{2}{ac}}+\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{c}^{\mathrm{2}} }{\mathrm{2}{ab}}? \\ $$

Question Number 84868 Answers: 1 Comments: 0

(√(1−cos^2 (((3π)/2)−x))) = −cos x+2(√3) sin (x−π)

$$\sqrt{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \left(\frac{\mathrm{3}\pi}{\mathrm{2}}−\mathrm{x}\right)}\:=\:−\mathrm{cos}\:\mathrm{x}+\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{sin}\:\left(\mathrm{x}−\pi\right) \\ $$

Question Number 84862 Answers: 2 Comments: 1

∫_( 0) ^(100) [tan^(−1) x]dx =? −Jakir Sarif Mondal.

$$\underset{\:\mathrm{0}} {\overset{\mathrm{100}} {\int}}\:\left[\mathrm{tan}^{−\mathrm{1}} {x}\right]{dx}\:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−\boldsymbol{{Jakir}}\:\boldsymbol{{Sarif}}\:\:\boldsymbol{{Mondal}}. \\ $$$$\:\:\:\:\:\:\: \\ $$

Question Number 84859 Answers: 0 Comments: 0

show that lim_(n→∞) ∫_0 ^1 ...∫_0 ^1 (n/(x_1 +x_2 +x_3 +...+x_n ))dx_1 dx_2 ...dx_n =2

$${show}\:{that} \\ $$$$\underset{{n}\rightarrow\infty} {{lim}}\int_{\mathrm{0}} ^{\mathrm{1}} ...\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{n}}{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} +{x}_{\mathrm{3}} +...+{x}_{{n}} }{dx}_{\mathrm{1}} {dx}_{\mathrm{2}} ...{dx}_{{n}} =\mathrm{2}\: \\ $$

Question Number 84849 Answers: 0 Comments: 5

ABC is a triangle prove that sinA+sinB+sinC>sinA sinB sinC

$${ABC}\:{is}\:{a}\:{triangle}\: \\ $$$${prove}\:{that} \\ $$$${sinA}+{sinB}+{sinC}>{sinA}\:{sinB}\:{sinC} \\ $$

Question Number 84845 Answers: 1 Comments: 1

Question Number 84843 Answers: 0 Comments: 2

∫((sin(7x))/(cos(3x))) dx

$$\int\frac{{sin}\left(\mathrm{7}{x}\right)}{{cos}\left(\mathrm{3}{x}\right)}\:{dx} \\ $$

Question Number 84835 Answers: 0 Comments: 1

Question Number 84834 Answers: 1 Comments: 1

lim_(x→0) ((√(x tan x))/(sin 3x))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}\:\mathrm{tan}\:\mathrm{x}}}{\mathrm{sin}\:\mathrm{3x}} \\ $$

Question Number 84830 Answers: 1 Comments: 0

(dy/dx) = ((1−x−y)/(x+y))

$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{1}−\mathrm{x}−\mathrm{y}}{\mathrm{x}+\mathrm{y}} \\ $$

Question Number 84828 Answers: 0 Comments: 1

log_3 (25x^2 −4)−log_3 (x) ≤ log_3 (26x^2 +((17)/x)−10)

$$\mathrm{log}_{\mathrm{3}} \left(\mathrm{25x}^{\mathrm{2}} −\mathrm{4}\right)−\mathrm{log}_{\mathrm{3}} \left(\mathrm{x}\right)\:\leqslant\:\mathrm{log}_{\mathrm{3}} \left(\mathrm{26x}^{\mathrm{2}} +\frac{\mathrm{17}}{\mathrm{x}}−\mathrm{10}\right) \\ $$

Question Number 84826 Answers: 0 Comments: 1

(√(x^2 −2x+2)) + log_3 (√(x^2 −2x+10)) = 2

$$\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{2}}\:+\:\mathrm{log}_{\mathrm{3}} \:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{10}}\:=\:\mathrm{2} \\ $$

Question Number 84820 Answers: 1 Comments: 0

Question Number 84814 Answers: 0 Comments: 1

1.Finx

$$\mathrm{1}.{Finx} \\ $$

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