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Question Number 165528 Answers: 1 Comments: 1

∫(1/(x+(√(x^2 +x+1))))dx

$$\int\frac{\mathrm{1}}{{x}+\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{dx} \\ $$

Question Number 165525 Answers: 0 Comments: 1

Question Number 165511 Answers: 0 Comments: 4

how do i find an irrational number between 0.124 and 0.125

$$\:\boldsymbol{{how}}\:\boldsymbol{{do}}\:\boldsymbol{{i}}\:\boldsymbol{{find}}\:\boldsymbol{{an}}\:\boldsymbol{{irrational}} \\ $$$$\boldsymbol{{number}}\:\boldsymbol{{between}}\:\:\mathrm{0}.\mathrm{124}\:\:\boldsymbol{{and}} \\ $$$$\mathrm{0}.\mathrm{125} \\ $$

Question Number 165505 Answers: 1 Comments: 0

Question Number 165503 Answers: 1 Comments: 0

y′(x)=((xln(y(x)))/(ln(x)y(x))) , y(x)=???.

$${y}'\left({x}\right)=\frac{{xln}\left({y}\left({x}\right)\right)}{{ln}\left({x}\right){y}\left({x}\right)}\:,\:{y}\left({x}\right)=???. \\ $$

Question Number 165493 Answers: 2 Comments: 0

calcul la somme de cette serie entiere Σ_(n=0) ^(+oo) ((2n+3)/(2n+1))x^n

$${calcul}\:{la}\:{somme}\:{de}\:{cette}\:{serie}\:{entiere} \\ $$$$\underset{{n}=\mathrm{0}} {\overset{+{oo}} {\sum}}\frac{\mathrm{2}{n}+\mathrm{3}}{\mathrm{2}{n}+\mathrm{1}}{x}^{{n}} \\ $$

Question Number 165483 Answers: 2 Comments: 1

Question Number 165480 Answers: 1 Comments: 0

Find the value of integers x, y which satisfy 9(x^2 + y^2 + 1) + 6xy = 2001

$${Find}\:\:{the}\:\:{value}\:\:{of}\:\:{integers}\:\:{x},\:{y}\:\:{which}\:\:{satisfy}\: \\ $$$$\:\:\:\:\mathrm{9}\left({x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:\mathrm{1}\right)\:+\:\mathrm{6}{xy}\:\:=\:\mathrm{2001} \\ $$

Question Number 165461 Answers: 0 Comments: 0

show that argth(x)=(1/2)ln(((1+x)/(1−x))) for x ∈ ]−1;1[

$${show}\:{that}\:{argth}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{2}}{ln}\left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right) \\ $$$$\left.{for}\:{x}\:\in\:\right]−\mathrm{1};\mathrm{1}\left[\right. \\ $$

Question Number 165471 Answers: 0 Comments: 1

{ ((h(3x)=(((2−x)/(x+1))−f(x^3 ))^2 )),((f(1)=f ′(1)=2)) :} h ′(3)=?

$$\:\begin{cases}{{h}\left(\mathrm{3}{x}\right)=\left(\frac{\mathrm{2}−{x}}{{x}+\mathrm{1}}−{f}\left({x}^{\mathrm{3}} \right)\right)^{\mathrm{2}} }\\{{f}\left(\mathrm{1}\right)={f}\:'\left(\mathrm{1}\right)=\mathrm{2}}\end{cases} \\ $$$$\:{h}\:'\left(\mathrm{3}\right)=? \\ $$

Question Number 165457 Answers: 1 Comments: 19

Question Number 165514 Answers: 1 Comments: 0

Question Number 165512 Answers: 0 Comments: 0

Σ_(n=0) ^∞ ((2n+1)/(e^((2n+1)π) +1))=^? (1/(24)) −−−−−−−−−−−−−−by Mr. Levent

$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{2}\boldsymbol{\mathrm{n}}+\mathrm{1}}{\boldsymbol{\mathrm{e}}^{\left(\mathrm{2}\boldsymbol{\mathrm{n}}+\mathrm{1}\right)\pi} +\mathrm{1}}\overset{?} {=}\frac{\mathrm{1}}{\mathrm{24}} \\ $$$$−−−−−−−−−−−−−−\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{Mr}}.\:\boldsymbol{\mathrm{Levent}} \\ $$

Question Number 165442 Answers: 1 Comments: 0

Question Number 165441 Answers: 1 Comments: 0

Question Number 165435 Answers: 1 Comments: 0

Question Number 165433 Answers: 1 Comments: 0

Question Number 165431 Answers: 2 Comments: 0

Question Number 165428 Answers: 1 Comments: 0

Question Number 165424 Answers: 0 Comments: 1

Question Number 165422 Answers: 0 Comments: 0

Question Number 165426 Answers: 0 Comments: 1

prove that ζ (0 )= ((−1)/2)

$$ \\ $$$$\:\:\:\:{prove}\:\:{that} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\zeta\:\left(\mathrm{0}\:\right)=\:\frac{−\mathrm{1}}{\mathrm{2}}\:\:\: \\ $$$$ \\ $$

Question Number 165419 Answers: 1 Comments: 0

Question Number 165418 Answers: 0 Comments: 0

prove that : 1^∗ : Σ_(n=1) ^∞ (( ζ (2n )−1)/( 1+ n)) = (3/(2 )) − ln (π ) 2^( ∗∗) : Σ_(n=2) ^∞ (( (−1)^( n) ( ζ (n )−1 ))/(1 + n))=(3/2) +(γ/2) −((ln(8π))/2) 3^( ∗∗) : Σ_(n=1) ^∞ (( ζ (2n )−1)/(1+ 2n)) = (3/2) −((ln(4π))/2) −−−− m.n −−−−

$$ \\ $$$$\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\mathrm{1}^{\ast} :\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\zeta\:\left(\mathrm{2}{n}\:\right)−\mathrm{1}}{\:\mathrm{1}+\:{n}}\:=\:\frac{\mathrm{3}}{\mathrm{2}\:}\:\:−\:\mathrm{ln}\:\left(\pi\:\right) \\ $$$$\:\:\:\mathrm{2}^{\:\ast\ast} :\:\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\right)^{\:{n}} \left(\:\:\zeta\:\left({n}\:\right)−\mathrm{1}\:\right)}{\mathrm{1}\:+\:{n}}=\frac{\mathrm{3}}{\mathrm{2}}\:+\frac{\gamma}{\mathrm{2}}\:−\frac{\mathrm{ln}\left(\mathrm{8}\pi\right)}{\mathrm{2}} \\ $$$$\:\:\:\mathrm{3}^{\:\ast\ast} \::\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\zeta\:\left(\mathrm{2}{n}\:\right)−\mathrm{1}}{\mathrm{1}+\:\mathrm{2}{n}}\:=\:\frac{\mathrm{3}}{\mathrm{2}}\:−\frac{\mathrm{ln}\left(\mathrm{4}\pi\right)}{\mathrm{2}}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−\:{m}.{n}\:−−−− \\ $$$$ \\ $$

Question Number 165404 Answers: 0 Comments: 9

given a loan from a bank on a fixed interest rate 5% suppose i want to make monthly payments for 14months how do i calculate the amount i should pay monthly and how do i know how much i will pay back to the bank at the end of the 14months? please i need explanations.

$$\mathrm{given}\:\mathrm{a}\:\mathrm{loan}\:\mathrm{from}\:\mathrm{a}\:\mathrm{bank}\:\mathrm{on}\:\mathrm{a}\:\mathrm{fixed}\:\mathrm{interest}\:\mathrm{rate}\:\mathrm{5\%} \\ $$$$\mathrm{suppose}\:\mathrm{i}\:\mathrm{want}\:\mathrm{to}\:\mathrm{make}\:\mathrm{monthly}\:\mathrm{payments}\:\mathrm{for}\:\mathrm{14months} \\ $$$$\mathrm{how}\:\mathrm{do}\:\mathrm{i}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{amount}\:\mathrm{i}\:\mathrm{should}\:\mathrm{pay}\:\mathrm{monthly}\:\mathrm{and} \\ $$$$\mathrm{how}\:\mathrm{do}\:\mathrm{i}\:\mathrm{know}\:\mathrm{how}\:\mathrm{much}\:\mathrm{i}\:\mathrm{will}\:\mathrm{pay}\:\mathrm{back}\:\mathrm{to}\:\mathrm{the}\:\mathrm{bank}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{14months}? \\ $$$$\mathrm{please}\:\mathrm{i}\:\mathrm{need}\:\mathrm{explanations}. \\ $$

Question Number 165403 Answers: 0 Comments: 0

sec^2 1° + sec^2 2° + sec^2 3° + …+ sec^2 89° = ?

$$\mathrm{sec}^{\mathrm{2}} \mathrm{1}°\:+\:\mathrm{sec}^{\mathrm{2}} \:\mathrm{2}°\:+\:\mathrm{sec}^{\mathrm{2}} \:\mathrm{3}°\:+\:\ldots+\:\mathrm{sec}^{\mathrm{2}} \:\mathrm{89}°\:=\:? \\ $$

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