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AllQuestion and Answers: Page 1222

Question Number 93315 Answers: 0 Comments: 0

If n>=2 and n⊂N . prove (1/2^2 )+(1/3^2 )+...(1/n^2 )<=n(1−(1/2)(1+(1/n)))^(1/n)

$${If}\:\:{n}>=\mathrm{2}\:\:{and}\:{n}\subset\mathbb{N}\:. \\ $$$${prove}\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+...\frac{\mathrm{1}}{{n}^{\mathrm{2}} }<={n}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\right)^{\frac{\mathrm{1}}{{n}}} \\ $$

Question Number 93312 Answers: 1 Comments: 0

(y−xy^2 )dx+(x+x^2 y^2 )dy = 0

$$\left(\mathrm{y}−\mathrm{xy}^{\mathrm{2}} \right)\mathrm{dx}+\left(\mathrm{x}+\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} \right)\mathrm{dy}\:=\:\mathrm{0}\: \\ $$

Question Number 93304 Answers: 5 Comments: 5

∫(√(tan (x)))dx Who can solve this problem?

$$\int\sqrt{\mathrm{tan}\:\left({x}\right)}{dx}\:{Who}\:{can}\:{solve}\:{this}\:{problem}? \\ $$

Question Number 93299 Answers: 0 Comments: 2

find a reduction formulae for I_n = ∫_(−1) ^0 x^n (1 + x)^2 dx

$$\mathrm{find}\:\mathrm{a}\:\mathrm{reduction}\:\mathrm{formulae}\:\mathrm{for}\:{I}_{{n}} \:=\:\int_{−\mathrm{1}} ^{\mathrm{0}} {x}^{{n}} \left(\mathrm{1}\:+\:{x}\right)^{\mathrm{2}} \:{dx} \\ $$

Question Number 93296 Answers: 1 Comments: 1

Question Number 93287 Answers: 0 Comments: 1

Question Number 93265 Answers: 1 Comments: 1

calculate ∫_0 ^((2π)/3) (dx/(3+sin(3x)))

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\mathrm{2}\pi}{\mathrm{3}}} \:\:\frac{{dx}}{\mathrm{3}+{sin}\left(\mathrm{3}{x}\right)} \\ $$

Question Number 93258 Answers: 1 Comments: 1

Question Number 93256 Answers: 0 Comments: 2

{ ((3 cos x = 4 cos y)),((3 sin x + 4sin y = 5)) :} find x &y with acute angle

$$\begin{cases}{\mathrm{3}\:\mathrm{cos}\:\mathrm{x}\:=\:\mathrm{4}\:\mathrm{cos}\:\mathrm{y}}\\{\mathrm{3}\:\mathrm{sin}\:\mathrm{x}\:+\:\mathrm{4sin}\:\mathrm{y}\:=\:\mathrm{5}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{x}\:\&\mathrm{y}\:\mathrm{with}\:\mathrm{acute}\:\mathrm{angle}\: \\ $$

Question Number 93283 Answers: 0 Comments: 0

(dy/dx) = 2x^2 +y^2 , y(0) = 1

$$\frac{{dy}}{{dx}}\:=\:\mathrm{2}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:,\:\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{1}\: \\ $$

Question Number 93284 Answers: 0 Comments: 5

Question Number 93249 Answers: 0 Comments: 4

calculate∫_0 ^((Π/2) ) (dx/(2+cos2x))

$${calculate}\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}\:} \frac{{dx}}{\mathrm{2}+{cos}\mathrm{2}{x}} \\ $$

Question Number 93248 Answers: 1 Comments: 1

∫ _0 ^1 ln(x) dx

$$\int\underset{\mathrm{0}} {\overset{\mathrm{1}} {\:}}\:\mathrm{ln}\left(\mathrm{x}\right)\:\mathrm{dx}\: \\ $$

Question Number 93241 Answers: 1 Comments: 0

(1+(1/x))^(x+1) =(1+(1/(2019)))^(2019) Find all possible values of x

$$\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}+\mathrm{1}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2019}}\right)^{\mathrm{2019}} \\ $$$$\mathrm{Find}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:{x} \\ $$

Question Number 93239 Answers: 2 Comments: 3

Calculate; i) cos(arctan x) ii) cos(arcsin x) iii) tan(arcsin x)

$$\mathrm{Calculate}; \\ $$$$\left.{i}\right)\:\mathrm{cos}\left(\mathrm{arctan}\:{x}\right) \\ $$$$\left.{ii}\right)\:\mathrm{cos}\left(\mathrm{arcsin}\:{x}\right) \\ $$$$\left.{iii}\right)\:\mathrm{tan}\left(\mathrm{arcsin}\:{x}\right) \\ $$

Question Number 93227 Answers: 0 Comments: 4

Question Number 93225 Answers: 0 Comments: 2

Question Number 93220 Answers: 0 Comments: 5

Please in an arithmetic mean a, A_1 , A_2 , A_3 , ... , A_n , b where A_1 , A_2 , A_3 , ... , A_n are nth arithmetic mean why is b = (n + 2)th term: like T_(n + 2) Please

Question Number 93209 Answers: 1 Comments: 6

Question Number 93208 Answers: 0 Comments: 8

Question Number 93204 Answers: 1 Comments: 1

Question Number 93203 Answers: 0 Comments: 1

what is the average area of a triangle formed by 3 random points in a 1×1 square?

$${what}\:{is}\:{the}\:{average}\:{area}\:{of}\:{a}\:{triangle} \\ $$$${formed}\:{by}\:\mathrm{3}\:{random}\:{points}\:{in}\:{a}\:\mathrm{1}×\mathrm{1} \\ $$$${square}? \\ $$

Question Number 93200 Answers: 1 Comments: 3

Question Number 93193 Answers: 1 Comments: 1

∫ ((ln(x+(√(x^2 −1))))/(√((x^2 −1)^3 ))) dx ?

$$\int\:\frac{\mathrm{ln}\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\right)}{\sqrt{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{3}} }}\:\mathrm{dx}\:?\: \\ $$

Question Number 93184 Answers: 0 Comments: 0

in solving the linear congruence ax ≡ b (mod n) ⇒ n∣(ax − b) ⇒ ax −b = kn ⇔ ax −kn = b ⇒ solving the linear diophantine equation ax −kn = b what are the general solution to the equation ax−kn = b

$$\mathrm{in}\:\mathrm{solving}\:\mathrm{the}\:\mathrm{linear}\:\mathrm{congruence} \\ $$$${ax}\:\equiv\:{b}\:\left(\mathrm{mod}\:{n}\right)\:\Rightarrow\:{n}\mid\left({ax}\:−\:{b}\right)\:\Rightarrow\:{ax}\:−{b}\:=\:{kn}\:\Leftrightarrow\:{ax}\:−{kn}\:=\:{b} \\ $$$$\Rightarrow\:\mathrm{solving}\:\mathrm{the}\:\mathrm{linear}\:\mathrm{diophantine}\:\mathrm{equation}\:{ax}\:−{kn}\:=\:{b} \\ $$$$\:\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:{ax}−{kn}\:=\:{b} \\ $$$$\: \\ $$$$ \\ $$

Question Number 93177 Answers: 0 Comments: 3

x^2 +(1/x^2 )=47 (√x)+(1/(√x))=...

$${x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=\mathrm{47} \\ $$$$\sqrt{{x}}+\frac{\mathrm{1}}{\sqrt{{x}}}=... \\ $$

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