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AllQuestion and Answers: Page 552

Question Number 154781 Answers: 0 Comments: 0

Question Number 154777 Answers: 1 Comments: 0

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

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

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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

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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

Question Number 154734 Answers: 1 Comments: 0

{ ((x=(y−2)(y+2))),((y=(z−2)(z+2))),((z=(x−2)(x+2))) :} ; x≠0, y≠0, z≠0 ⇒ x^5 +y^5 +z^5 =?

$$\:\begin{cases}{\mathrm{x}=\left(\mathrm{y}−\mathrm{2}\right)\left(\mathrm{y}+\mathrm{2}\right)}\\{\mathrm{y}=\left(\mathrm{z}−\mathrm{2}\right)\left(\mathrm{z}+\mathrm{2}\right)}\\{\mathrm{z}=\left(\mathrm{x}−\mathrm{2}\right)\left(\mathrm{x}+\mathrm{2}\right)}\end{cases}\:;\:\mathrm{x}\neq\mathrm{0},\:\mathrm{y}\neq\mathrm{0},\:\mathrm{z}\neq\mathrm{0} \\ $$$$\Rightarrow\:\mathrm{x}^{\mathrm{5}} +\mathrm{y}^{\mathrm{5}} +\mathrm{z}^{\mathrm{5}} \:=? \\ $$

Question Number 154729 Answers: 0 Comments: 0

Question Number 154725 Answers: 1 Comments: 0

If f(x)=x^3 +x+1 then invrse function of f(x) is???

$${If}\:{f}\left({x}\right)={x}^{\mathrm{3}} +{x}+\mathrm{1}\:{then}\:{invrse}\:{function} \\ $$$${of}\:{f}\left({x}\right)\:{is}??? \\ $$

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Question Number 154723 Answers: 0 Comments: 3

G = (√(46−27i)) +(√(−4−3i)) G^2 =?

$$\:{G}\:=\:\sqrt{\mathrm{46}−\mathrm{27}{i}}\:+\sqrt{−\mathrm{4}−\mathrm{3}{i}} \\ $$$$\:{G}^{\mathrm{2}} \:=? \\ $$

Question Number 154719 Answers: 1 Comments: 0

lim_(x→(π/6)) ((2ln [Γ(sin x)]−ln π)/(Γ(sec x)−1)) =?

$$\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{6}}} {\mathrm{lim}}\:\frac{\mathrm{2ln}\:\left[\Gamma\left(\mathrm{sin}\:{x}\right)\right]−\mathrm{ln}\:\pi}{\Gamma\left(\mathrm{sec}\:{x}\right)−\mathrm{1}}\:=? \\ $$

Question Number 154710 Answers: 0 Comments: 0

Find: lim_(n→∞) ((((n+1)^2 )/( ((2(n+1)!))^(1/(n+1)) )) - (n^2 /( ((2n!))^(1/n) ))) = ?

$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{2}} }{\:\sqrt[{\boldsymbol{\mathrm{n}}+\mathrm{1}}]{\mathrm{2}\left(\mathrm{n}+\mathrm{1}\right)!}}\:-\:\frac{\mathrm{n}^{\mathrm{2}} }{\:\sqrt[{\boldsymbol{\mathrm{n}}}]{\mathrm{2n}!}}\right)\:=\:? \\ $$

Question Number 154677 Answers: 1 Comments: 10

Solve for real numbers: ((x^9 - 256x^3 - 791)/(84x^3 )) = ((4x + 7))^(1/3)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\frac{\mathrm{x}^{\mathrm{9}} \:-\:\mathrm{256x}^{\mathrm{3}} \:-\:\mathrm{791}}{\mathrm{84x}^{\mathrm{3}} }\:=\:\sqrt[{\mathrm{3}}]{\mathrm{4x}\:+\:\mathrm{7}} \\ $$

Question Number 154675 Answers: 1 Comments: 0

if we let f(n) = (n/2) (n + 1) then solve the equation for real numbers f(f(f(f(n)))) = (1/(32))

$$\mathrm{if}\:\mathrm{we}\:\mathrm{let} \\ $$$$\mathrm{f}\left(\mathrm{n}\right)\:=\:\frac{\mathrm{n}}{\mathrm{2}}\:\left(\mathrm{n}\:+\:\mathrm{1}\right) \\ $$$$\mathrm{then}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\mathrm{f}\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{f}\left(\mathrm{n}\right)\right)\right)\right)\:=\:\frac{\mathrm{1}}{\mathrm{32}} \\ $$

Question Number 154673 Answers: 0 Comments: 2

∫ln(sinx)dx=?

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

Question Number 154672 Answers: 1 Comments: 0

how many positive x≤10 000 integers are such that 2^x −x^2 is divisible by 7?

$$\: \\ $$$$\:\mathrm{how}\:\mathrm{many}\:\mathrm{positive}\:{x}\leqslant\mathrm{10}\:\mathrm{000}\:\mathrm{integers}\:\mathrm{are}\:\: \\ $$$$\:\mathrm{such}\:\mathrm{that}\:\mathrm{2}^{{x}} −{x}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{7}? \\ $$$$\: \\ $$

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If f(x)=f(x−1)+f(x+1) where f(10)=6 and f(20)=2f(21) then f(16)=…?

$$\:{If}\:{f}\left({x}\right)={f}\left({x}−\mathrm{1}\right)+{f}\left({x}+\mathrm{1}\right)\:{where} \\ $$$${f}\left(\mathrm{10}\right)=\mathrm{6}\:{and}\:{f}\left(\mathrm{20}\right)=\mathrm{2}{f}\left(\mathrm{21}\right) \\ $$$${then}\:{f}\left(\mathrm{16}\right)=\ldots? \\ $$

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