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Question Number 120810 Answers: 1 Comments: 0

Determine the convergence intervval of : Σ_(n = 0) ^∞ (−1)^n (x − 1)^n

$${Determine}\:{the}\:{convergence}\:{intervval}\:{of}\:: \\ $$$$\underset{{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \:\left({x}\:−\:\mathrm{1}\right)^{{n}} \\ $$

Question Number 120809 Answers: 0 Comments: 0

Find the largest number of positive integers that can be found in such a way that any two of them a and b ( a≠b) satisfy the next inequality ∣a−b∣≥((ab)/(100))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{number}\:\mathrm{of}\:\mathrm{positive} \\ $$$$\mathrm{integers}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\:\mathrm{found}\:\mathrm{in}\:\mathrm{such}\:\mathrm{a}\:\mathrm{way} \\ $$$$\mathrm{that}\:\mathrm{any}\:\mathrm{two}\:\mathrm{of}\:\mathrm{them}\:{a}\:\mathrm{and}\:{b}\:\left(\:{a}\neq{b}\right)\: \\ $$$$\mathrm{satisfy}\:\mathrm{the}\:\mathrm{next}\:\mathrm{inequality}\:\mid{a}−{b}\mid\geqslant\frac{{ab}}{\mathrm{100}} \\ $$

Question Number 120801 Answers: 1 Comments: 2

Question Number 120800 Answers: 0 Comments: 1

what remain when we divise 2222^(3333 ) by 3333^(2222)

$${what}\:{remain}\:{when}\:{we}\:{divise} \\ $$$$\mathrm{2222}^{\mathrm{3333}\:} {by}\:\mathrm{3333}^{\mathrm{2222}} \\ $$

Question Number 120797 Answers: 0 Comments: 1

Question Number 120791 Answers: 0 Comments: 0

Question Number 120790 Answers: 0 Comments: 1

Question Number 120789 Answers: 0 Comments: 0

Question Number 120780 Answers: 2 Comments: 2

solve x^2^x =−(1/2)

$${solve}\:{x}^{\mathrm{2}^{{x}} } =−\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 120775 Answers: 2 Comments: 0

...advanced calculus... evaluate :: Φ=^(???) ∫_0 ^( 1) ln(x)tan^(−1) (x)dx ...m.n.1970...

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:...{advanced}\:\:{calculus}... \\ $$$$\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Phi\overset{???} {=}\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left({x}\right){tan}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:...{m}.{n}.\mathrm{1970}... \\ $$

Question Number 120774 Answers: 1 Comments: 0

...advanced calculus... prove that :: Ω=∫_0 ^( 1) ((ln(x))/( ((1−x^3 ))^(1/3) ))dx=^(???) −(π/(3(√3)))(ln(3)+(π/(3(√3)))) ...m.n.1970...

$$\:\:\:\:\:\:\:\:\:\:...{advanced}\:\:{calculus}... \\ $$$$\:\:\:\:\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left({x}\right)}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}−{x}^{\mathrm{3}} }}{dx}\overset{???} {=}−\frac{\pi}{\mathrm{3}\sqrt{\mathrm{3}}}\left({ln}\left(\mathrm{3}\right)+\frac{\pi}{\mathrm{3}\sqrt{\mathrm{3}}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...{m}.{n}.\mathrm{1970}... \\ $$

Question Number 120773 Answers: 1 Comments: 0

Question Number 120768 Answers: 0 Comments: 0

Question Number 120769 Answers: 2 Comments: 0

1).x^2 −5=(√(13+x)) ,Find x=? 2).x^3 +3x^2 −x−4=0 ,Find x=?

$$\left.\mathrm{1}\right).\mathrm{x}^{\mathrm{2}} −\mathrm{5}=\sqrt{\mathrm{13}+\mathrm{x}}\:\:,\mathrm{Find}\:\mathrm{x}=? \\ $$$$\left.\mathrm{2}\right).\mathrm{x}^{\mathrm{3}} +\mathrm{3x}^{\mathrm{2}} −\mathrm{x}−\mathrm{4}=\mathrm{0}\:\:,\mathrm{Find}\:\mathrm{x}=? \\ $$

Question Number 120761 Answers: 1 Comments: 0

∫ tan^(−1) ((√((1−x)/(1+x))) ) dx ?

$$\:\:\:\:\int\:\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}}\:\right)\:\mathrm{dx}\:? \\ $$

Question Number 120758 Answers: 3 Comments: 0

∫ (dx/(a sin x + b cos x))

$$\:\int\:\frac{\mathrm{dx}}{{a}\:\mathrm{sin}\:\mathrm{x}\:+\:{b}\:\mathrm{cos}\:\mathrm{x}} \\ $$

Question Number 120755 Answers: 0 Comments: 0

Question Number 120748 Answers: 2 Comments: 0

Question Number 120745 Answers: 1 Comments: 0

Question Number 120729 Answers: 1 Comments: 0

Question Number 120727 Answers: 1 Comments: 0

Question Number 120724 Answers: 1 Comments: 2

Question Number 120721 Answers: 2 Comments: 2

Question Number 120720 Answers: 2 Comments: 0

Given lim_(x→∞) (√(x+2(√x)+3)) −(√x)+b = 4 find the value of b^2 +1

$$\:\mathrm{Given}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{x}+\mathrm{2}\sqrt{\mathrm{x}}+\mathrm{3}}\:−\sqrt{\mathrm{x}}+\mathrm{b}\:=\:\mathrm{4} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{b}^{\mathrm{2}} +\mathrm{1} \\ $$

Question Number 120715 Answers: 0 Comments: 0

Question Number 120711 Answers: 3 Comments: 0

show that 1+2+3+4...=((−1)/8)

$${show}\:{that}\:\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}...=\frac{−\mathrm{1}}{\mathrm{8}} \\ $$

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