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Question Number 224233    Answers: 1   Comments: 0

Prove that ∀n≥2 e^(2n−1) −1 ≥ 2n(2n−1)

$$\mathrm{Prove}\:\mathrm{that}\:\forall\mathrm{n}\geqslant\mathrm{2} \\ $$$$\mathrm{e}^{\mathrm{2n}−\mathrm{1}} −\mathrm{1}\:\geqslant\:\mathrm{2n}\left(\mathrm{2n}−\mathrm{1}\right) \\ $$

Question Number 224229    Answers: 1   Comments: 1

Question Number 224225    Answers: 0   Comments: 0

Question Number 224224    Answers: 0   Comments: 3

Question Number 224213    Answers: 1   Comments: 1

Question Number 224207    Answers: 0   Comments: 5

Question Number 224203    Answers: 0   Comments: 6

Question Number 224201    Answers: 0   Comments: 0

∫ (x^3 /(x^7 −8x^2 )) dx

$$\int\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{7}} −\mathrm{8x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$

Question Number 224191    Answers: 0   Comments: 1

Question Number 224197    Answers: 2   Comments: 0

∫_0 ^∞ (e^(−𝛟x^2 ) +e^(−𝛅x^2 ) +e^(−𝛄x^2 ) ) 𝛄−euler′s mascheroni constant 𝛟−golden ratio 𝛅−silver ratio klipto−quanta♠

$$\int_{\mathrm{0}} ^{\infty} \left(\boldsymbol{\mathrm{e}}^{−\boldsymbol{\varphi\mathrm{x}}^{\mathrm{2}} } +\boldsymbol{\mathrm{e}}^{−\boldsymbol{\delta\mathrm{x}}^{\mathrm{2}} } +\boldsymbol{\mathrm{e}}^{−\boldsymbol{\gamma\mathrm{x}}^{\mathrm{2}} } \right) \\ $$$$\boldsymbol{\gamma}−\boldsymbol{\mathrm{euler}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{mascheroni}}\:\boldsymbol{\mathrm{constant}} \\ $$$$\boldsymbol{\varphi}−\boldsymbol{\mathrm{golden}}\:\boldsymbol{\mathrm{ratio}} \\ $$$$\boldsymbol{\delta}−\boldsymbol{\mathrm{silver}}\:\boldsymbol{\mathrm{ratio}} \\ $$$$\boldsymbol{\mathrm{klipto}}−\boldsymbol{\mathrm{quanta}}\spadesuit \\ $$

Question Number 224182    Answers: 1   Comments: 0

Calculate I=∫ ((sin x)/(1+ sin x)) dx

$$\mathrm{Calculate} \\ $$$${I}=\int\:\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\:\mathrm{sin}\:{x}}\:\mathrm{d}{x} \\ $$

Question Number 224176    Answers: 2   Comments: 1

Question Number 224168    Answers: 2   Comments: 1

Question Number 224160    Answers: 0   Comments: 0

Q224122

$${Q}\mathrm{224122} \\ $$

Question Number 224153    Answers: 0   Comments: 8

Question Number 224150    Answers: 0   Comments: 2

Question Number 224146    Answers: 1   Comments: 0

a = 12^(223) ∙ 7^(56) + 19^(25) what is the last digit of the number?

$$\boldsymbol{\mathrm{a}}\:=\:\mathrm{12}^{\mathrm{223}} \:\centerdot\:\mathrm{7}^{\mathrm{56}} \:+\:\mathrm{19}^{\mathrm{25}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number}? \\ $$

Question Number 224144    Answers: 1   Comments: 1

Question Number 224124    Answers: 2   Comments: 0

∫_(−2) ^2 ((x^3 cos((x/2))+(1/2))/( (√(4−x^2 ))))

$$\int_{−\mathrm{2}} ^{\mathrm{2}} \frac{\boldsymbol{\mathrm{x}}^{\mathrm{3}} \boldsymbol{\mathrm{cos}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)+\frac{\mathrm{1}}{\mathrm{2}}}{\:\sqrt{\mathrm{4}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }} \\ $$

Question Number 224122    Answers: 1   Comments: 1

Question Number 224121    Answers: 1   Comments: 0

Question Number 224118    Answers: 1   Comments: 0

Question Number 224113    Answers: 0   Comments: 0

Guys my exams are finished ! I will be active as usual! :)

$${Guys}\:{my}\:{exams}\:{are}\:{finished}\:! \\ $$$${I}\:{will}\:{be}\:{active}\:{as}\:{usual}! \\ $$$$\left.:\right) \\ $$

Question Number 224108    Answers: 3   Comments: 0

Question Number 224106    Answers: 0   Comments: 1

Question Number 224100    Answers: 1   Comments: 0

Calculate I=∫^( +∞) _( 0) [(1/t)−(1/(sh(t)))]^( 2) dt

$$\mathrm{Calculate}\:\mathrm{I}=\underset{\:\mathrm{0}} {\int}^{\:+\infty} \left[\frac{\mathrm{1}}{\mathrm{t}}−\frac{\mathrm{1}}{\mathrm{sh}\left(\mathrm{t}\right)}\right]^{\:\mathrm{2}} \mathrm{dt} \\ $$

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