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Question Number 154860 Answers: 0 Comments: 0

(1/(n+1))+(1/(n+2))+(1/(n+3))+...+(1/(2n))<(3/4) n>1 Prove that

$$\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{n}+\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{n}+\mathrm{3}}+...+\frac{\mathrm{1}}{\mathrm{2n}}<\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{n}>\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$

Question Number 154857 Answers: 1 Comments: 0

Question Number 154854 Answers: 1 Comments: 1

Question Number 154853 Answers: 1 Comments: 0

Question Number 154851 Answers: 0 Comments: 7

Question Number 154849 Answers: 1 Comments: 0

ax + y + z = 1 x + ay + z = a x + y + az = a^2 Find value of x, y, z in a .

$${ax}\:+\:{y}\:+\:{z}\:=\:\mathrm{1} \\ $$$${x}\:+\:{ay}\:+\:{z}\:=\:{a} \\ $$$${x}\:+\:{y}\:+\:{az}\:=\:{a}^{\mathrm{2}} \\ $$$${Find}\:\:{value}\:\:{of}\:\:{x},\:{y},\:{z}\:\:\:{in}\:\:{a}\:. \\ $$

Question Number 154846 Answers: 0 Comments: 2

y′=((y cos(x))/(1+2y^2 )) trouve la solution de lequation differentielle

$${y}'=\frac{{y}\:{cos}\left({x}\right)}{\mathrm{1}+\mathrm{2}{y}^{\mathrm{2}} } \\ $$$${trouve}\:{la}\:{solution}\:{de}\:{lequation}\:{differentielle} \\ $$

Question Number 154823 Answers: 1 Comments: 0

∫_0 ^( ∞) (e^(−x) /( x^(3/4) )) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{e}^{−{x}} }{\:{x}^{\frac{\mathrm{3}}{\mathrm{4}}} \:}\:{dx} \\ $$$$\: \\ $$

Question Number 154824 Answers: 1 Comments: 0

Σ_(k=0) ^∞ ((4^(−k) Γ(k))/(k!))

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{4}^{−{k}} \Gamma\left({k}\right)}{{k}!} \\ $$$$\: \\ $$

Question Number 154805 Answers: 0 Comments: 2

Question Number 154804 Answers: 2 Comments: 1

Solve for real numbers: ((5(√5) + x))^(1/5) - ((5(√5) - x))^(1/5) = (2)^(1/5)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\sqrt[{\mathrm{5}}]{\mathrm{5}\sqrt{\mathrm{5}}\:+\:\mathrm{x}}\:-\:\sqrt[{\mathrm{5}}]{\mathrm{5}\sqrt{\mathrm{5}}\:-\:\mathrm{x}}\:=\:\sqrt[{\mathrm{5}}]{\mathrm{2}} \\ $$

Question Number 154794 Answers: 0 Comments: 1

Question Number 154786 Answers: 0 Comments: 0

((sin(x+60°))/(sin60°))+((sin(x+60°)∙sin30°)/(sin(2x+30°)∙sin60°))=((sinx)/(sin60°))+1 x∈(0;60°) x=?

$$\frac{\mathrm{sin}\left(\mathrm{x}+\mathrm{60}°\right)}{\mathrm{sin60}°}+\frac{\mathrm{sin}\left(\mathrm{x}+\mathrm{60}°\right)\centerdot\mathrm{sin30}°}{\mathrm{sin}\left(\mathrm{2x}+\mathrm{30}°\right)\centerdot\mathrm{sin60}°}=\frac{\mathrm{sinx}}{\mathrm{sin60}°}+\mathrm{1} \\ $$$$\mathrm{x}\in\left(\mathrm{0};\mathrm{60}°\right)\:\:\mathrm{x}=? \\ $$

Question Number 154785 Answers: 0 Comments: 3

soit: y′+tan(x)y=sin(2x) ,avec f(0)=1 alors f(π)=?

$${soit}:\:{y}'+{tan}\left({x}\right){y}={sin}\left(\mathrm{2}{x}\right)\:,{avec} \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{1}\:\:\:{alors}\:{f}\left(\pi\right)=? \\ $$

Question Number 154780 Answers: 3 Comments: 0

∫_(−∞) ^( ∞) (1/(x^4 +x^3 +x^2 +1)) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{1}}{{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +\mathrm{1}}\:{dx} \\ $$$$\: \\ $$

Question Number 154781 Answers: 0 Comments: 0

Question Number 154777 Answers: 1 Comments: 0

Question Number 154776 Answers: 0 Comments: 1

lim_(x→∞) (1+((1−((sin ((1/x)))/(1/x)))/(e−(1+(1/x))^x )))^x =?

$$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}−\frac{\mathrm{sin}\:\left(\frac{\mathrm{1}}{{x}}\right)}{\frac{\mathrm{1}}{{x}}}}{{e}−\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}} }\right)^{{x}} =? \\ $$

Question Number 154773 Answers: 0 Comments: 0

Question Number 154791 Answers: 1 Comments: 0

Question Number 154758 Answers: 0 Comments: 0

if x;y;z≥0 and x^2 +y^2 +z^2 =1 then prove that: ((x + y + z)/(1 + xy)) ≤ (√2)

$$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\geqslant\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{1} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}}{\mathrm{1}\:+\:\mathrm{xy}}\:\leqslant\:\sqrt{\mathrm{2}} \\ $$

Question Number 154749 Answers: 0 Comments: 0

Question Number 154748 Answers: 1 Comments: 0

Question Number 154741 Answers: 0 Comments: 4

I danced, its a bit calculus based! I am all praises for Caro Emerald′s songs.

$${I}\:{danced},\:{its}\:{a}\:{bit}\:{calculus}\:{based}! \\ $$$${I}\:{am}\:{all}\:{praises}\:{for}\:{Caro}\: \\ $$$${Emerald}'{s}\:{songs}. \\ $$

Question Number 154740 Answers: 1 Comments: 0

A man will be (x+10) years in 8 years time. If 2 years ago he was 63 years, find the value of x.

$$\mathrm{A}\:\mathrm{man}\:\mathrm{will}\:\mathrm{be}\:\left({x}+\mathrm{10}\right)\:\mathrm{years}\:\mathrm{in}\:\mathrm{8}\:\mathrm{years}\:\mathrm{time}. \\ $$$$\mathrm{If}\:\mathrm{2}\:\mathrm{years}\:\mathrm{ago}\:\mathrm{he}\:\mathrm{was}\:\mathrm{63}\:\mathrm{years},\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:{x}. \\ $$

Question Number 154736 Answers: 1 Comments: 1

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