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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!))

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

Question Number 150226 Answers: 2 Comments: 0

prove that :: ζ (0 )=^? ((−1)/2) ..........■ m.n...

$$ \\ $$$$\:\:\:\:\:\mathrm{prove}\:\:\mathrm{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\zeta\:\left(\mathrm{0}\:\right)\overset{?} {=}\:\frac{−\mathrm{1}}{\mathrm{2}}\:..........\blacksquare \\ $$$$\:\:\:\:\:\:\:{m}.{n}... \\ $$

Question Number 150121 Answers: 1 Comments: 0

Find in closed form: n∈N^∗ ∫_( 0) ^( 1) ln(1 - x^2 )ln^n (1 - x) dx = ?

$$\mathrm{Find}\:\mathrm{in}\:\mathrm{closed}\:\mathrm{form}:\:\:\mathrm{n}\in\mathbb{N}^{\ast} \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\mathrm{ln}\left(\mathrm{1}\:-\:\mathrm{x}^{\mathrm{2}} \right)\mathrm{ln}^{\boldsymbol{\mathrm{n}}} \left(\mathrm{1}\:-\:\mathrm{x}\right)\:\mathrm{dx}\:=\:? \\ $$

Question Number 150119 Answers: 2 Comments: 0

Find the smallest value of a given expression: (x^2 + 6x + 8)^2 + 5

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{given} \\ $$$$\mathrm{expression}: \\ $$$$\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{6x}\:+\:\mathrm{8}\right)^{\mathrm{2}} \:+\:\mathrm{5} \\ $$

Question Number 150103 Answers: 1 Comments: 0

Ω = ∫_0 ^( π) sin^( (1/2)) (x). ln( sin (x) )dx=?

$$\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\pi} {sin}^{\:\frac{\mathrm{1}}{\mathrm{2}}} \left({x}\right).\:\mathrm{ln}\left(\:{sin}\:\left({x}\right)\:\right){dx}=? \\ $$$$ \\ $$

Question Number 150097 Answers: 1 Comments: 0

Question Number 150079 Answers: 2 Comments: 0

∫(dx/((x^2 +x+1)^2 ))

$$\int\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 150064 Answers: 1 Comments: 0

How can i evaluate the value of ∫_2 ^( 4) (e^t /t)dt = ?

$$\mathrm{How}\:\mathrm{can}\:\mathrm{i}\:\mathrm{evaluate}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\: \\ $$$$\:\:\int_{\mathrm{2}} ^{\:\mathrm{4}} \frac{\mathrm{e}^{\mathrm{t}} }{\mathrm{t}}\mathrm{dt}\:=\:? \\ $$

Question Number 150063 Answers: 0 Comments: 0

Question Number 150062 Answers: 2 Comments: 0

Question Number 150059 Answers: 2 Comments: 0

Σ_(n=1) ^∞ (1/(n∙(2n + 1))) = ?

$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}\centerdot\left(\mathrm{2n}\:+\:\mathrm{1}\right)}\:=\:? \\ $$

Question Number 150058 Answers: 2 Comments: 2

Solve the equation: cos^4 (x) + i sin^4 (x) = 4e^(4ix)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{cos}^{\mathrm{4}} \left(\mathrm{x}\right)\:+\:\mathrm{i}\:\mathrm{sin}^{\mathrm{4}} \left(\mathrm{x}\right)\:=\:\mathrm{4e}^{\mathrm{4}\boldsymbol{\mathrm{ix}}} \\ $$

Question Number 150056 Answers: 2 Comments: 1

Question Number 150053 Answers: 0 Comments: 0

let x;y;z;t>0 and x+y+z+t=4 prove that (4/((xyzt)^2 )) + 3 ≥ (√(45 + x^4 + y^4 + z^4 + t^4 ))

$$\mathrm{let}\:\:\mathrm{x};\mathrm{y};\mathrm{z};\mathrm{t}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{x}+\mathrm{y}+\mathrm{z}+\mathrm{t}=\mathrm{4} \\ $$$$\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{4}}{\left(\mathrm{xyzt}\right)^{\mathrm{2}} }\:+\:\mathrm{3}\:\geqslant\:\sqrt{\mathrm{45}\:+\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:+\:\mathrm{z}^{\mathrm{4}} \:+\:\mathrm{t}^{\mathrm{4}} } \\ $$

Question Number 150045 Answers: 0 Comments: 0

Question Number 150044 Answers: 2 Comments: 0

Given f(((2x−3)/(2x+1)))+f(((2x+3)/(1−2x)))= 4x f(x)=?

$$\:\mathrm{Given}\:\mathrm{f}\left(\frac{\mathrm{2x}−\mathrm{3}}{\mathrm{2x}+\mathrm{1}}\right)+\mathrm{f}\left(\frac{\mathrm{2x}+\mathrm{3}}{\mathrm{1}−\mathrm{2x}}\right)=\:\mathrm{4x} \\ $$$$\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$

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