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Question Number 93091    Answers: 0   Comments: 1

Find the sum: Σ_(n=1) ^(2020) 2^2^n

$${Find}\:{the}\:{sum}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\mathrm{2020}} {\sum}}\mathrm{2}^{\mathrm{2}^{{n}} } \\ $$

Question Number 93071    Answers: 1   Comments: 0

Question Number 95059    Answers: 0   Comments: 22

To Tinku Tara dear sir: i experienced following issues: 1. sometimes i got notification, but i didn′t see any update in the corresponding threads. what can be the reason? 2. when i activate the filter to show bookmarked posts, only some of the bookmarked posts will be displayed, others not. 3. it takes long time (some minutes, even hang up ) when the app updates after i have edited a post, added an image. (see picture below) 4. (old problem) when i leave the app just temporarily to go to an other app, the app starts again and i don′t come back to the place where i was before.

$${To}\:{Tinku}\:{Tara} \\ $$$${dear}\:{sir}:\:{i}\:{experienced}\:{following}\:{issues}: \\ $$$$\mathrm{1}.\:{sometimes}\:{i}\:{got}\:{notification},\:{but} \\ $$$${i}\:{didn}'{t}\:{see}\:{any}\:{update}\:{in}\:{the} \\ $$$${corresponding}\:{threads}.\:{what}\:{can}\:{be} \\ $$$${the}\:{reason}? \\ $$$$\mathrm{2}.\:{when}\:{i}\:{activate}\:{the}\:{filter}\:{to}\:{show} \\ $$$${bookmarked}\:{posts},\:{only}\:{some}\:{of}\:{the} \\ $$$${bookmarked}\:{posts}\:{will}\:{be}\:{displayed}, \\ $$$${others}\:{not}. \\ $$$$\mathrm{3}.\:{it}\:{takes}\:{long}\:{time}\:\left({some}\:{minutes},\right. \\ $$$$\left.{even}\:{hang}\:{up}\:\right)\:{when}\:{the}\:{app}\:{updates} \\ $$$${after}\:{i}\:{have}\:{edited}\:{a}\:{post},\:{added}\:{an} \\ $$$${image}.\:\left({see}\:{picture}\:{below}\right) \\ $$$$\mathrm{4}.\:\left({old}\:{problem}\right)\:{when}\:{i}\:{leave}\:{the}\:{app} \\ $$$${just}\:{temporarily}\:{to}\:{go}\:{to}\:{an}\:{other} \\ $$$${app},\:{the}\:{app}\:{starts}\:{again}\:{and}\:{i}\:{don}'{t} \\ $$$${come}\:{back}\:{to}\:{the}\:{place}\:{where}\:{i}\:{was} \\ $$$${before}. \\ $$

Question Number 93064    Answers: 1   Comments: 7

prove that (d/dx)x^n =nx^(n−1)

$${prove}\:{that}\: \\ $$$$\frac{{d}}{{dx}}{x}^{{n}} ={nx}^{{n}−\mathrm{1}} \\ $$

Question Number 93061    Answers: 0   Comments: 3

∫_1 ^(+∞) ((sin u)/u)du

$$\int_{\mathrm{1}} ^{+\infty} \frac{\mathrm{sin}\:\mathrm{u}}{\mathrm{u}}\mathrm{du} \\ $$

Question Number 93059    Answers: 1   Comments: 0

y^′ +2xy=cos x+2x sin x

$$\mathrm{y}^{'} +\mathrm{2xy}=\mathrm{cos}\:\mathrm{x}+\mathrm{2x}\:\mathrm{sin}\:\mathrm{x} \\ $$

Question Number 93057    Answers: 1   Comments: 1

y=b1x1+b2x2+c i need to arrange the equation for thd value of x2

$${y}={b}\mathrm{1}{x}\mathrm{1}+{b}\mathrm{2}{x}\mathrm{2}+{c} \\ $$$${i}\:{need}\:{to}\:{arrange}\:{the}\:{equation}\:{for}\:{thd}\:{value}\:{of}\:{x}\mathrm{2} \\ $$

Question Number 93045    Answers: 1   Comments: 2

∫ sin^(−1) ((√(x/2))) dx

$$\int\:\mathrm{sin}^{−\mathrm{1}} \left(\sqrt{\frac{{x}}{\mathrm{2}}}\right)\:{dx}\: \\ $$

Question Number 93044    Answers: 1   Comments: 2

is (8/9) is the multiplicative inerse of −1 (1/8)? why or why not?

$$\mathrm{is}\:\frac{\mathrm{8}}{\mathrm{9}}\:\mathrm{is}\:\mathrm{the}\:\mathrm{multiplicative}\:\mathrm{inerse}\:\mathrm{of}\:−\mathrm{1}\:\frac{\mathrm{1}}{\mathrm{8}}? \\ $$$$\mathrm{why}\:\mathrm{or}\:\mathrm{why}\:\mathrm{not}? \\ $$

Question Number 93039    Answers: 0   Comments: 1

{ ((xy+yz = 8)),((yz+xz = 9)),((zx+xy = 5)) :}

$$\begin{cases}{{xy}+{yz}\:=\:\mathrm{8}}\\{{yz}+{xz}\:=\:\mathrm{9}}\\{{zx}+{xy}\:=\:\mathrm{5}}\end{cases} \\ $$

Question Number 93038    Answers: 1   Comments: 1

∫_1 ^5 (√(x^3 +1)) dx = ?

$$\underset{\mathrm{1}} {\overset{\mathrm{5}} {\int}}\:\sqrt{\mathrm{x}^{\mathrm{3}} +\mathrm{1}}\:\mathrm{dx}\:=\:? \\ $$

Question Number 93033    Answers: 0   Comments: 3

lim_(x→π/6) (tan (((3x)/2)))^(tan (3x)) =?

$$\underset{{x}\rightarrow\pi/\mathrm{6}} {\mathrm{lim}}\:\left(\mathrm{tan}\:\left(\frac{\mathrm{3x}}{\mathrm{2}}\right)\right)^{\mathrm{tan}\:\left(\mathrm{3x}\right)} =?\: \\ $$

Question Number 93031    Answers: 1   Comments: 11

Question Number 93077    Answers: 1   Comments: 1

Se f((√x) −1) = x+6, log[f(1)] = ?

$$\:\:\mathrm{Se}\:\:\mathrm{f}\left(\sqrt{\mathrm{x}}\:−\mathrm{1}\right)\:=\:\mathrm{x}+\mathrm{6},\:\:\mathrm{log}\left[\mathrm{f}\left(\mathrm{1}\right)\right]\:=\:? \\ $$

Question Number 93081    Answers: 0   Comments: 3

Solve x^y =y^x x, y ∈ N

$$\mathrm{Solve}\:\mathrm{x}^{\mathrm{y}} =\mathrm{y}^{\mathrm{x}} \:\:\:\mathrm{x},\:\mathrm{y}\:\in\:\mathbb{N} \\ $$

Question Number 93005    Answers: 1   Comments: 0

∫ sec x (√(sec x+tan x)) dx =

$$\int\:\mathrm{sec}\:\mathrm{x}\:\sqrt{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\:=\: \\ $$

Question Number 93003    Answers: 1   Comments: 0

(x^2 −2xy−y^2 )dx−(x−y)^2 dy=0

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

Question Number 92997    Answers: 1   Comments: 0

Question Number 92993    Answers: 0   Comments: 1

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

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

Question Number 92987    Answers: 2   Comments: 0

{ (((√y) + ln (x^2 )=2)),((y + 4 ln(x) =28)) :}

$$\begin{cases}{\sqrt{\mathrm{y}}\:+\:\mathrm{ln}\:\left(\mathrm{x}^{\mathrm{2}} \right)=\mathrm{2}}\\{\mathrm{y}\:+\:\mathrm{4}\:\mathrm{ln}\left(\mathrm{x}\right)\:=\mathrm{28}}\end{cases} \\ $$

Question Number 93004    Answers: 0   Comments: 0

∫ ((sin^(−1) (sin (x)))/(sin^4 (x)+cos^2 (x))) dx ?

$$\int\:\frac{\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:\left(\mathrm{x}\right)\right)}{\mathrm{sin}\:^{\mathrm{4}} \left(\mathrm{x}\right)+\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{x}\right)}\:\mathrm{dx}\:? \\ $$

Question Number 92980    Answers: 1   Comments: 0

log _((9x))^(1/(3 )) ((√(x^3 /3))) + log _((3x^2 ))^(1/(3 )) ((√(27x))) ≤ 3

$$\mathrm{log}\:_{\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}{x}}} \:\left(\sqrt{\frac{{x}^{\mathrm{3}} }{\mathrm{3}}}\right)\:+\:\mathrm{log}\:_{\sqrt[{\mathrm{3}\:\:}]{\mathrm{3}{x}^{\mathrm{2}} }} \left(\sqrt{\mathrm{27}{x}}\right)\:\leqslant\:\mathrm{3} \\ $$

Question Number 92976    Answers: 1   Comments: 0

define Δ_n =((n(1+n))/2) find a closer form for Σ_(n=1) ^∞ (1/Δ_n ^m )

$${define} \\ $$$$\Delta_{{n}} =\frac{{n}\left(\mathrm{1}+{n}\right)}{\mathrm{2}} \\ $$$${find}\:{a}\:{closer}\:{form}\:{for} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\Delta_{{n}} ^{{m}} } \\ $$

Question Number 92971    Answers: 0   Comments: 3

1) decompose F(x) =(1/(x^4 (x−3)^5 )) 2)calculate ∫_5 ^(+∞) (dx/(x^4 (x−3)^5 ))

$$\left.\mathrm{1}\right)\:{decompose}\:{F}\left({x}\right)\:=\frac{\mathrm{1}}{{x}^{\mathrm{4}} \left({x}−\mathrm{3}\right)^{\mathrm{5}} } \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{5}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{4}} \left({x}−\mathrm{3}\right)^{\mathrm{5}} } \\ $$

Question Number 92966    Answers: 0   Comments: 3

lim_(x→−∞) ((6x+5)/(√(9x^2 +4x−2))) ?

$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\frac{\mathrm{6x}+\mathrm{5}}{\sqrt{\mathrm{9x}^{\mathrm{2}} +\mathrm{4x}−\mathrm{2}}}\:? \\ $$

Question Number 92960    Answers: 2   Comments: 0

∫ ((sin^2 x dx)/((1+cos x)^2 ))

$$\int\:\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx}}{\left(\mathrm{1}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} }\: \\ $$

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