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Question Number 100565 Answers: 1 Comments: 1

Question Number 100562 Answers: 0 Comments: 0

Question Number 100561 Answers: 1 Comments: 1

Question Number 100557 Answers: 2 Comments: 0

Ω=∫_0 ^∞ (e^(ax) /(e^(bx) +1))dx, b>a

$$\Omega=\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{e}^{{ax}} }{{e}^{{bx}} +\mathrm{1}}{dx},\:{b}>{a} \\ $$

Question Number 100538 Answers: 0 Comments: 1

Question Number 100540 Answers: 0 Comments: 1

Question Number 100539 Answers: 0 Comments: 2

(−1)^n Σ_(n=1) ^∞ (3^n /n)

$$\left(−\mathrm{1}\right)^{{n}} \underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{3}^{{n}} }{{n}} \\ $$

Question Number 100543 Answers: 2 Comments: 1

Question Number 100522 Answers: 1 Comments: 0

Question Number 100514 Answers: 2 Comments: 0

calculatelim_(n→+∞) ∫_0 ^∞ (1−(x/n))^n ln(1+2x)dx

$$\mathrm{calculatelim}_{\mathrm{n}\rightarrow+\infty} \:\int_{\mathrm{0}} ^{\infty} \:\left(\mathrm{1}−\frac{\mathrm{x}}{\mathrm{n}}\right)^{\mathrm{n}} \mathrm{ln}\left(\mathrm{1}+\mathrm{2x}\right)\mathrm{dx} \\ $$

Question Number 100513 Answers: 0 Comments: 0

findA_(nm) =∫_0 ^∞ e^(−nx) ∣sin(px)∣ dx with n and p integr natural ≥1

$$\mathrm{findA}_{\mathrm{nm}} \:=\int_{\mathrm{0}} ^{\infty} \:\:\mathrm{e}^{−\mathrm{nx}} \:\mid\mathrm{sin}\left(\mathrm{px}\right)\mid\:\mathrm{dx}\:\:\mathrm{with}\:\:\mathrm{n}\:\mathrm{and}\:\mathrm{p}\:\mathrm{integr}\:\mathrm{natural}\:\geqslant\mathrm{1} \\ $$

Question Number 100512 Answers: 0 Comments: 0

calculate ∫_(−∞) ^(+∞) (x^n /((x^2 +x+1)^n )) dx with n integr and n≥2

$$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{x}^{\mathrm{n}} }{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)^{\mathrm{n}} }\:\mathrm{dx}\:\:\mathrm{with}\:\mathrm{n}\:\mathrm{integr}\:\mathrm{and}\:\mathrm{n}\geqslant\mathrm{2} \\ $$

Question Number 100511 Answers: 1 Comments: 0

calculate ∫_(−∞) ^∞ ((arctan(cosx +sinx))/(x^2 +4)) dx

$$\mathrm{calculate}\:\:\int_{−\infty} ^{\infty} \:\:\frac{\mathrm{arctan}\left(\mathrm{cosx}\:+\mathrm{sinx}\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}}\:\mathrm{dx} \\ $$

Question Number 100498 Answers: 0 Comments: 0

Question Number 100528 Answers: 1 Comments: 2

Question Number 100492 Answers: 2 Comments: 3

((16−((64)/(16−((64)/(16−((64)/(16−...))))))))^(1/(3 )) −((−2−(1/(−2−(1/(−2−(1/(−2−...))))))))^(1/(3 ))

$$\sqrt[{\mathrm{3}\:\:\:}]{\mathrm{16}−\frac{\mathrm{64}}{\mathrm{16}−\frac{\mathrm{64}}{\mathrm{16}−\frac{\mathrm{64}}{\mathrm{16}−...}}}}−\sqrt[{\mathrm{3}\:\:}]{−\mathrm{2}−\frac{\mathrm{1}}{−\mathrm{2}−\frac{\mathrm{1}}{−\mathrm{2}−\frac{\mathrm{1}}{−\mathrm{2}−...}}}} \\ $$

Question Number 100491 Answers: 1 Comments: 0

Question Number 100479 Answers: 0 Comments: 0

Please How to calculate the focusing latitude of a microscope?

$${Please}\:{How}\:{to}\:{calculate}\:{the}\:{focusing} \\ $$$${latitude}\:{of}\:{a}\:{microscope}? \\ $$

Question Number 100464 Answers: 1 Comments: 4

A car is driving. It most arrive at destination situated at 2046 m. It has travelled 2m the first day, 4 m the second, 8m the thirst, 16 the fourth day ... How many days is necessary to arrive at destination?

$${A}\:{car}\:{is}\:{driving}.\:{It}\:{most}\:{arrive} \\ $$$${at}\:{destination}\:{situated}\:{at}\:\mathrm{2046}\:{m}. \\ $$$${It}\:{has}\:{travelled}\:\mathrm{2}{m}\:{the}\:{first}\:{day},\: \\ $$$$\mathrm{4}\:{m}\:{the}\:{second},\:\mathrm{8}{m}\:{the}\:{thirst},\:\mathrm{16} \\ $$$${the}\:{fourth}\:{day}\:... \\ $$$${How}\:{many}\:{days}\:{is}\:{necessary}\:\:{to}\: \\ $$$${arrive}\:{at}\:{destination}? \\ $$

Question Number 100465 Answers: 1 Comments: 1

There are two numbers n_(1 ) and n_(2 ) . they are composed by three digits. the sum of 3 digits that compose n_1 is 15. the first digit of n_(2 ) is the second digit of n_1 and the first digit of n_1 is also the second digit of n_(2 ) . we know also that n_1 is a prime number and we know also that n_1 is divisible by 5 and n_1 −n_2 =306. 1) find n_1 and n_(2.) Sorry, the first digit of n_(1 ) and n_2 is ≠0

$${There}\:{are}\:{two}\:{numbers}\:{n}_{\mathrm{1}\:} {and}\:{n}_{\mathrm{2}\:\:\:\:\:\:} . \\ $$$${they}\:{are}\:{composed}\:{by}\:{three}\:{digits}. \\ $$$${the}\:{sum}\:{of}\:\mathrm{3}\:{digits}\:{that}\:{compose}\:{n}_{\mathrm{1}} \\ $$$$\:{is}\:\:\mathrm{15}.\:{the}\:{first}\:{digit}\:{of}\:{n}_{\mathrm{2}\:} {is}\:{the}\: \\ $$$${second}\:{digit}\:{of}\:{n}_{\mathrm{1}} \:{and}\:{the}\:{first}\: \\ $$$${digit}\:{of}\:{n}_{\mathrm{1}} \:{is}\:{also}\:{the}\:{second}\:{digit}\:{of} \\ $$$${n}_{\mathrm{2}\:} .\:{we}\:{know}\:{also}\:{that}\:{n}_{\mathrm{1}} \:{is}\:{a}\:{prime} \\ $$$${number}\:{and}\:{we}\:{know}\:{also}\:{that}\:{n}_{\mathrm{1}} {is} \\ $$$${divisible}\:{by}\:\mathrm{5}\:{and}\:{n}_{\mathrm{1}} −{n}_{\mathrm{2}} =\mathrm{306}. \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:{find}\:{n}_{\mathrm{1}} {and}\:{n}_{\mathrm{2}.} \\ $$$$ \\ $$$${Sorry},\:{the}\:{first}\:{digit}\:{of}\:{n}_{\mathrm{1}\:} {and}\:{n}_{\mathrm{2}} \:{is}\:\neq\mathrm{0} \\ $$

Question Number 100468 Answers: 3 Comments: 0

Σ_(n=1) ^∞ (n/((2n+1)!)) help me pls

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}}{\left(\mathrm{2}{n}+\mathrm{1}\right)!} \\ $$$${help}\:{me}\:{pls} \\ $$

Question Number 100450 Answers: 1 Comments: 0