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AllQuestion and Answers: Page 207

Question Number 198025 Answers: 1 Comments: 1

Question Number 198023 Answers: 1 Comments: 0

Question Number 198022 Answers: 1 Comments: 0

Five letters are selected from

$$\:\:\mathrm{Five}\:\mathrm{letters}\:\mathrm{are}\:\mathrm{selected}\:\mathrm{from} \\ $$

Question Number 198018 Answers: 1 Comments: 0

Question Number 198014 Answers: 1 Comments: 0

Question Number 198013 Answers: 1 Comments: 0

Question Number 198001 Answers: 0 Comments: 2

∫(e)^((x)^(lnx) ) dx=?

$$\int\left({e}\right)^{\left({x}\right)^{{lnx}} } \:{dx}=? \\ $$

Question Number 197998 Answers: 3 Comments: 0

lim_(x→0) ((x−ln(x+(√(1+x^2 ))))/x^3 )=? with out L′Hospital rul

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}−{ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)}{{x}^{\mathrm{3}} }=? \\ $$$${with}\:{out}\:{L}'{Hospital}\:{rul} \\ $$

Question Number 197985 Answers: 0 Comments: 5

lim_(n→∞) ( _( k) ^( n) ) p^k q^(n−k)

$$\underset{{n}\rightarrow\infty} {{lim}}\:\left(\underset{\:{k}} {\overset{\:\:{n}} {\:}}\:\right)\:{p}^{{k}} \:{q}^{{n}−{k}} \\ $$

Question Number 197982 Answers: 2 Comments: 0

Question Number 197980 Answers: 1 Comments: 4

Question Number 197972 Answers: 0 Comments: 0

Find L^(−1) { (1/(2^( s) (√( 2s+1)) )) }= ? inverse laplace transform...

$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:{Find}\: \\ $$$$\:\:\:\:\:\:\:\mathscr{L}\:^{−\mathrm{1}} \left\{\:\:\frac{\mathrm{1}}{\mathrm{2}^{\:{s}} \:\sqrt{\:\mathrm{2}{s}+\mathrm{1}}\:}\:\right\}=\:? \\ $$$$ \\ $$$$\:\:\:\:\:\:{inverse}\:\:{laplace}\:{transform}... \\ $$

Question Number 197970 Answers: 2 Comments: 0

Question Number 197967 Answers: 1 Comments: 0

Question Number 197961 Answers: 0 Comments: 4

A cylindrical container is designed to contain bees. At exactly 12:00pm, there are 2 bees in the container. At every 1 min, the total number of bees in the container is doubled. By 1.00pm, the container is full of bees. At what time is the container A. Half full of the bees B. Quarter full of the bees C. 1/8th full of the bees D. 1/16th full of the bees Note: you can assume any size of the cylindrical container, and all bees are of equal size. Show working

$$ \\ $$A cylindrical container is designed to contain bees. At exactly 12:00pm, there are 2 bees in the container. At every 1 min, the total number of bees in the container is doubled. By 1.00pm, the container is full of bees. At what time is the container A. Half full of the bees B. Quarter full of the bees C. 1/8th full of the bees D. 1/16th full of the bees Note: you can assume any size of the cylindrical container, and all bees are of equal size. Show working

Question Number 197960 Answers: 1 Comments: 0

determiner le total de nombres de 5 chiffres comprises entre 10000 et 50000 divisibles simultanement par 5 et 9 (sans utiliser les formules d arrangement et de combinaison)

$$\mathrm{determiner}\:\mathrm{le}\:\mathrm{total}\:\mathrm{de}\:\mathrm{nombres}\:\mathrm{de}\: \\ $$$$\mathrm{5}\:\mathrm{chiffres}\:\mathrm{comprises}\:\mathrm{entre}\:\mathrm{10000}\:\mathrm{et}\: \\ $$$$\mathrm{50000}\:\:\mathrm{divisibles}\:\mathrm{simultanement}\:\mathrm{par} \\ $$$$\mathrm{5}\:\mathrm{et}\:\mathrm{9}\:\:\: \\ $$$$\left(\mathrm{sans}\:\mathrm{utiliser}\:\mathrm{les}\:\mathrm{formules}\:\mathrm{d}\:\mathrm{arrangement}\right. \\ $$$$\left.\mathrm{et}\:\mathrm{de}\:\mathrm{combinaison}\right) \\ $$$$ \\ $$

Question Number 197951 Answers: 0 Comments: 0

Σ_(n=1 ) ^∞ (n/(n^4 +n^2 +1)) − Σ_(n=1) ^∞ (n^2 /(n^8 +n^4 +1)) = ?

$$\:\underset{{n}=\mathrm{1}\:} {\overset{\infty} {\sum}}\frac{{n}}{{n}^{\mathrm{4}} +{n}^{\mathrm{2}} +\mathrm{1}}\:−\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{n}^{\mathrm{2}} }{{n}^{\mathrm{8}} +{n}^{\mathrm{4}} +\mathrm{1}}\:=\:? \\ $$

Question Number 197950 Answers: 0 Comments: 0

Let x,y,z>0 , x+y+z=3 Prove That : (1/( (√(x^2 +2x))))+(1/( (√(z^2 +2z))))+(√3)((1/(y+2))−(y/9))+((((√x)+(√y)+(√z)+24))^(1/3) /( (√3)))≥((17)/(3(√3)))

$${Let}\:{x},{y},{z}>\mathrm{0}\:,\:{x}+{y}+{z}=\mathrm{3}\:{Prove}\:{That}\:: \\ $$$$\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}}}+\frac{\mathrm{1}}{\:\sqrt{{z}^{\mathrm{2}} +\mathrm{2}{z}}}+\sqrt{\mathrm{3}}\left(\frac{\mathrm{1}}{{y}+\mathrm{2}}−\frac{{y}}{\mathrm{9}}\right)+\frac{\sqrt[{\mathrm{3}}]{\sqrt{{x}}+\sqrt{{y}}+\sqrt{{z}}+\mathrm{24}}}{\:\sqrt{\mathrm{3}}}\geqslant\frac{\mathrm{17}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$

Question Number 197947 Answers: 1 Comments: 0

calculate… L = lim _(n→∞) (( (1+(1/2) )(1+(1/3))… (1+(1/n))))^(1/n) = ?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{calculate}\ldots \\ $$$$\:\:\mathrm{L}\:=\:\mathrm{lim}\:_{\mathrm{n}\rightarrow\infty} \sqrt[{{n}}]{\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\:\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}\right)\ldots\:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)}\:=\:?\:\:\:\:\:\:\:\: \\ $$$$\:\: \\ $$

Question Number 197944 Answers: 1 Comments: 0

tan(π/(12))=((sinα−sin(π/(12)))/(cosα+cos(π/(12)))) α=?

$${tan}\frac{\pi}{\mathrm{12}}=\frac{{sin}\alpha−{sin}\frac{\pi}{\mathrm{12}}}{{cos}\alpha+{cos}\frac{\pi}{\mathrm{12}}} \\ $$$$\alpha=? \\ $$

Question Number 197937 Answers: 1 Comments: 0

(√3) sin^2 θ∙tanβ+cos^2 β=?

$$\sqrt{\mathrm{3}}\:{sin}^{\mathrm{2}} \theta\centerdot{tan}\beta+{cos}^{\mathrm{2}} \beta=? \\ $$

Question Number 197935 Answers: 1 Comments: 0

Show that Σ_(n=1) ^∞ (((n!)^2 )/((2n)!)) =(1/3)+((2π(√3))/(27))