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Question Number 150223 Answers: 2 Comments: 0

Question Number 150222 Answers: 1 Comments: 0

Calcul des sommes A− Σ_(p=0) ^α C_n ^(2p) =.....?? avec α=E((n/2)) B− Σ_(p=0) ^β C_n ^(2p+1) =....?? avec β=E(((n−1)/2))

$${Calcul}\:{des}\:{sommes} \\ $$$${A}−\:\underset{{p}=\mathrm{0}} {\overset{\alpha} {\sum}}{C}_{{n}} ^{\mathrm{2}{p}} =.....??\:\:\:\:\:{avec}\:\:\alpha={E}\left(\frac{{n}}{\mathrm{2}}\right) \\ $$$${B}−\:\underset{{p}=\mathrm{0}} {\overset{\beta} {\sum}}{C}_{{n}} ^{\mathrm{2}{p}+\mathrm{1}} =....??\:\:\:\:{avec}\:\beta={E}\left(\frac{{n}−\mathrm{1}}{\mathrm{2}}\right) \\ $$$$ \\ $$

Question Number 150531 Answers: 0 Comments: 6

Find x;y ; x∈Q and y∈Z such that: 2020(x^2 + y^2 ) + 2019(x + y) = 2021xy

$$\mathrm{Find}\:\:\mathrm{x};\mathrm{y}\:\:;\:\:\mathrm{x}\in\mathrm{Q}\:\:\mathrm{and}\:\:\mathrm{y}\in\mathrm{Z}\:\:\mathrm{such}\:\mathrm{that}: \\ $$$$\mathrm{2020}\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)\:+\:\mathrm{2019}\left(\mathrm{x}\:+\:\mathrm{y}\right)\:=\:\mathrm{2021xy} \\ $$

Question Number 150324 Answers: 0 Comments: 0

Calcul des sommes A− Σ_(p=0) ^α C_n ^(2p) =..... avec α=E((n/2)) B− Σ_(p=0) ^β C_n ^(2p+1) =..... avec β=E(((n−1)/2))

$${Calcul}\:{des}\:{sommes} \\ $$$${A}−\:\:\underset{{p}=\mathrm{0}} {\overset{\alpha} {\sum}}{C}_{{n}} ^{\mathrm{2}{p}} =.....\:\:{avec}\:\:\alpha={E}\left(\frac{{n}}{\mathrm{2}}\right) \\ $$$${B}−\:\underset{{p}=\mathrm{0}} {\overset{\beta} {\sum}}{C}_{{n}} ^{\mathrm{2}{p}+\mathrm{1}} =.....\:\:{avec}\:\beta={E}\left(\frac{{n}−\mathrm{1}}{\mathrm{2}}\right) \\ $$

Question Number 150533 Answers: 1 Comments: 0

solve... I:= ∫_(−∞) ^( ∞) e^( x−n.sinh^( 2) (x)) dx =^(??) (√(π/n)) ...m.n...

$$\:\:\:\: \\ $$$$\:\:\:\:\mathrm{solve}... \\ $$$$\:\:\mathrm{I}:=\:\int_{−\infty} ^{\:\infty} {e}^{\:{x}−{n}.{sinh}^{\:\mathrm{2}} \left({x}\right)} {dx}\:\overset{??} {=}\sqrt{\frac{\pi}{{n}}} \\ $$$$\:\:\:\:\:\:\:...{m}.{n}... \\ $$

Question Number 150202 Answers: 2 Comments: 1

lim_(x→2) (((16−4^x )/(9−3^x ))) with out lophital

$${lim}_{{x}\rightarrow\mathrm{2}} \left(\frac{\mathrm{16}−\mathrm{4}^{{x}} }{\mathrm{9}−\mathrm{3}^{{x}} }\right)\:{with}\:{out}\:{lophital} \\ $$

Question Number 150199 Answers: 0 Comments: 1

Question Number 150191 Answers: 2 Comments: 0

{ ((x - (√y) = 7)),((y + (√x) = 7)) :} ⇒ xy = ?

$$\begin{cases}{\mathrm{x}\:-\:\sqrt{\mathrm{y}}\:=\:\mathrm{7}}\\{\mathrm{y}\:+\:\sqrt{\mathrm{x}}\:=\:\mathrm{7}}\end{cases}\:\:\:\Rightarrow\:\:\mathrm{xy}\:=\:? \\ $$

Question Number 150189 Answers: 1 Comments: 1

Solve the equation: (x - 3) (√(x^2 - x − 2)) = 0

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\left(\mathrm{x}\:-\:\mathrm{3}\right)\:\sqrt{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{x}\:−\:\mathrm{2}}\:=\:\mathrm{0} \\ $$

Question Number 150187 Answers: 2 Comments: 1

If f(x) = 2x^2 + 5 ⇒ f^( −1) (2) = ?

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{2x}^{\mathrm{2}} \:+\:\mathrm{5}\:\:\Rightarrow\:\:\mathrm{f}^{\:−\mathrm{1}} \left(\mathrm{2}\right)\:=\:? \\ $$

Question Number 150186 Answers: 1 Comments: 0

If f(x) = sin^4 (3x) ⇒ f^′ ((π/(12))) = ?

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{sin}^{\mathrm{4}} \left(\mathrm{3x}\right)\:\:\Rightarrow\:\:{f}\:^{'} \left(\frac{\pi}{\mathrm{12}}\right)\:=\:? \\ $$

Question Number 150181 Answers: 1 Comments: 0

(x−6)^3 +(x−5)^3 +(x−4)^3 =3(x−6)(x−5)(x−4) x=?

$$\:\left(\mathrm{x}−\mathrm{6}\right)^{\mathrm{3}} +\left(\mathrm{x}−\mathrm{5}\right)^{\mathrm{3}} +\left(\mathrm{x}−\mathrm{4}\right)^{\mathrm{3}} =\mathrm{3}\left(\mathrm{x}−\mathrm{6}\right)\left(\mathrm{x}−\mathrm{5}\right)\left(\mathrm{x}−\mathrm{4}\right) \\ $$$$\mathrm{x}=? \\ $$

Question Number 150180 Answers: 1 Comments: 0

show that derivative of Sin x/x =1

$$\mathrm{show}\:\mathrm{that}\:\mathrm{derivative}\:\mathrm{of}\:\mathrm{Sin}\:\mathrm{x}/\mathrm{x}\:=\mathrm{1} \\ $$$$ \\ $$

Question Number 150177 Answers: 1 Comments: 5

Question Number 150171 Answers: 1 Comments: 0

solve in R: (((ax−b)^3 ))^(1/7) −(((b−ax)^(−3) ))^(1/7) =((65)/8)

$${solve}\:{in}\:\mathbb{R}: \\ $$$$\sqrt[{\mathrm{7}}]{\left({ax}−{b}\right)^{\mathrm{3}} }−\sqrt[{\mathrm{7}}]{\left({b}−{ax}\right)^{−\mathrm{3}} }=\frac{\mathrm{65}}{\mathrm{8}} \\ $$

Question Number 150165 Answers: 0 Comments: 0

Question Number 150156 Answers: 2 Comments: 0

Question Number 150311 Answers: 1 Comments: 0

x,y ∈ R Find all functions that satisfy this condition : f(x+y) = f(x) ∙ f(y) − f(x ∙ y) + 1 Find all functions that satisfy this condition : f(f(x)) = f(x) + x

$${x},{y}\:\in\:\mathbb{R} \\ $$$${Find}\:\:{all}\:{functions}\:\:{that}\:\:{satisfy}\:\:{this}\:\:{condition}\:: \\ $$$${f}\left({x}+{y}\right)\:=\:{f}\left({x}\right)\:\centerdot\:{f}\left({y}\right)\:−\:{f}\left({x}\:\centerdot\:{y}\right)\:+\:\mathrm{1} \\ $$$$ \\ $$$${Find}\:\:{all}\:{functions}\:\:{that}\:\:{satisfy}\:\:{this}\:\:{condition}\:: \\ $$$${f}\left({f}\left({x}\right)\right)\:=\:{f}\left({x}\right)\:+\:{x} \\ $$

Question Number 150482 Answers: 0 Comments: 2

(1/(cos^4 (𝛑/7))) + (1/(cos^4 ((2𝛑)/7))) + (1/(cos^4 ((3𝛑)/7))) = ?

$$\frac{\mathrm{1}}{\mathrm{cos}^{\mathrm{4}} \:\frac{\boldsymbol{\pi}}{\mathrm{7}}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{cos}^{\mathrm{4}} \:\frac{\mathrm{2}\boldsymbol{\pi}}{\mathrm{7}}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{cos}^{\mathrm{4}} \:\frac{\mathrm{3}\boldsymbol{\pi}}{\mathrm{7}}}\:\:=\:\:? \\ $$

Question Number 150154 Answers: 0 Comments: 0

1)The probability of a Malaria patient surviving from a newly discovered drug is 0.27,while the probability of a typhoid patient surviving from another newly discovered drug is 0.85.Find the probabilities of i)Either of the two patient surviving ii)Neither of the two patient surviving iii)At least one survives

$$\left.\mathrm{1}\right)\mathrm{The}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{a}\:\mathrm{Malaria}\:\mathrm{patient}\: \\ $$$$\mathrm{surviving}\:\mathrm{from}\:\mathrm{a}\:\mathrm{newly}\:\mathrm{discovered} \\ $$$$\mathrm{drug}\:\mathrm{is}\:\mathrm{0}.\mathrm{27},\mathrm{while}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{typhoid}\:\mathrm{patient}\:\mathrm{surviving}\:\mathrm{from}\:\mathrm{another} \\ $$$$\mathrm{newly}\:\mathrm{discovered}\:\mathrm{drug}\:\mathrm{is}\:\mathrm{0}.\mathrm{85}.\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{probabilities}\:\mathrm{of}\: \\ $$$$\left.\mathrm{i}\right)\mathrm{Either}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{patient}\:\mathrm{surviving} \\ $$$$\left.\mathrm{ii}\right)\mathrm{Neither}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{patient}\:\mathrm{surviving} \\ $$$$\left.\mathrm{iii}\right)\mathrm{At}\:\mathrm{least}\:\mathrm{one}\:\mathrm{survives} \\ $$

Question Number 150150 Answers: 1 Comments: 4

Question Number 150136 Answers: 1 Comments: 1

Question Number 150135 Answers: 1 Comments: 0

4n^2 +2n=e^n

$$\mathrm{4}{n}^{\mathrm{2}} +\mathrm{2}{n}={e}^{{n}} \\ $$

Question Number 150263 Answers: 2 Comments: 2

Π_(k=1) ^n (1+(k^2 /n^2 ))^(1/n)

$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}+\frac{{k}^{\mathrm{2}} }{{n}^{\mathrm{2}} }\right)^{\frac{\mathrm{1}}{{n}}} \\ $$

Question Number 150125 Answers: 0 Comments: 0

∫ (x^( 2) /( (√(4+x^( 4) )))) dx=?

$$ \\ $$$$\:\:\:\:\int\:\frac{{x}^{\:\mathrm{2}} }{\:\sqrt{\mathrm{4}+{x}^{\:\mathrm{4}} }}\:{dx}=? \\ $$

Question Number 150721 Answers: 2 Comments: 0

calculate the convergence interval of the serie Σ_(n=0) ^∞ (((−1)^n x^(2n) )/(n!))

$${calculate}\:{the}\:{convergence}\:{interval}\:{of}\:{the} \\ $$$${serie} \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{2}{n}} }{{n}!} \\ $$

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