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Question Number 101419    Answers: 2   Comments: 0

y′′−4y′+3y = (e^x /(1+e^x ))

$$\mathrm{y}''−\mathrm{4y}'+\mathrm{3y}\:=\:\frac{\mathrm{e}^{\mathrm{x}} }{\mathrm{1}+\mathrm{e}^{\mathrm{x}} } \\ $$

Question Number 101418    Answers: 0   Comments: 6

Find 2020 term from series (1/1),(2/1),(1/2),(3/1),(2/2),(1/3),(4/1),(3/2),(2/3),(1/4) ,(5/1),(4/2),... is ___ (A) ((2019)/(2020)) (B) ((61)/4) (C)((63)/1) (D) ((96)/4) (E) ((2020)/(2019))

$$\mathrm{Find}\:\mathrm{2020}\:\mathrm{term}\:\mathrm{from}\:\mathrm{series} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}},\frac{\mathrm{2}}{\mathrm{1}},\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{3}}{\mathrm{1}},\frac{\mathrm{2}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{3}},\frac{\mathrm{4}}{\mathrm{1}},\frac{\mathrm{3}}{\mathrm{2}},\frac{\mathrm{2}}{\mathrm{3}},\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$,\frac{\mathrm{5}}{\mathrm{1}},\frac{\mathrm{4}}{\mathrm{2}},...\:\mathrm{is}\:\_\_\_ \\ $$$$\left(\mathrm{A}\right)\:\frac{\mathrm{2019}}{\mathrm{2020}}\:\:\:\:\:\:\left(\mathrm{B}\right)\:\frac{\mathrm{61}}{\mathrm{4}}\:\:\:\:\:\left(\mathrm{C}\right)\frac{\mathrm{63}}{\mathrm{1}} \\ $$$$\left(\mathrm{D}\right)\:\frac{\mathrm{96}}{\mathrm{4}}\:\:\:\:\:\:\left(\mathrm{E}\right)\:\frac{\mathrm{2020}}{\mathrm{2019}} \\ $$

Question Number 101409    Answers: 0   Comments: 1

which is correct ∫((5x^4 +4x^5 )/((x^5 +x+1)^2 )) dx is equal to a) (x^5 /(x^5 +x+1)) b)−((x+1)/(x^5 +x+1))

$$\mathrm{which}\:\mathrm{is}\:\mathrm{correct} \\ $$$$\int\frac{\mathrm{5x}^{\mathrm{4}} +\mathrm{4x}^{\mathrm{5}} }{\left(\mathrm{x}^{\mathrm{5}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left.\mathrm{a}\left.\right)\:\frac{\mathrm{x}^{\mathrm{5}} }{\mathrm{x}^{\mathrm{5}} +\mathrm{x}+\mathrm{1}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{b}\right)−\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}^{\mathrm{5}} +\mathrm{x}+\mathrm{1}} \\ $$

Question Number 101393    Answers: 1   Comments: 0

Question Number 101400    Answers: 0   Comments: 4

App Updates: Show and Hide Keyboard Request by teachers using this app along with screen sharing apps for online classes Set Home Screen to Forum Requested by Mr W

$$\mathrm{App}\:\mathrm{Updates}: \\ $$$$\boldsymbol{\mathrm{Show}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{Hide}}\:\boldsymbol{\mathrm{Keyboard}} \\ $$$$\mathrm{Request}\:\mathrm{by}\:\mathrm{teachers}\:\mathrm{using}\:\mathrm{this} \\ $$$$\mathrm{app}\:\mathrm{along}\:\mathrm{with}\:\mathrm{screen}\:\mathrm{sharing}\:\mathrm{apps} \\ $$$$\mathrm{for}\:\mathrm{online}\:\mathrm{classes} \\ $$$$\boldsymbol{\mathrm{Set}}\:\boldsymbol{\mathrm{Home}}\:\boldsymbol{\mathrm{Screen}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{Forum}} \\ $$$$\mathrm{Requested}\:\mathrm{by}\:\mathrm{Mr}\:\mathrm{W} \\ $$

Question Number 101382    Answers: 2   Comments: 0

Question Number 105239    Answers: 1   Comments: 0

Σ_(Σ_(p=5) ^6 p) ^(Σ_(p=8) ^(11) p) ∫_(11) ^(13) (((12ky)/x^2 ) + 6x) dx = Σ_(Σ_(p=4) ^7 p) ^(Σ_(p=9) ^(12) p) ∫_(11) ^(16) (x^2 y−(3/2)k)dx solve for y

$$\underset{\underset{{p}=\mathrm{5}} {\overset{\mathrm{6}} {\sum}}{p}} {\overset{\underset{{p}=\mathrm{8}} {\overset{\mathrm{11}} {\sum}}{p}} {\sum}}\:\underset{\mathrm{11}} {\overset{\mathrm{13}} {\int}}\left(\frac{\mathrm{12}{ky}}{{x}^{\mathrm{2}} }\:+\:\mathrm{6}{x}\right)\:{dx}\:=\:\underset{\underset{{p}=\mathrm{4}} {\overset{\mathrm{7}} {\sum}}{p}} {\overset{\underset{{p}=\mathrm{9}} {\overset{\mathrm{12}} {\sum}}{p}} {\sum}}\:\underset{\mathrm{11}} {\overset{\mathrm{16}} {\int}}\left({x}^{\mathrm{2}} {y}−\frac{\mathrm{3}}{\mathrm{2}}{k}\right){dx} \\ $$$${solve}\:{for}\:{y} \\ $$

Question Number 105238    Answers: 1   Comments: 0

(dy/dx) = (1/(3e^y −2x)) ?

$$\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{1}}{\mathrm{3}{e}^{{y}} −\mathrm{2}{x}}\:? \\ $$

Question Number 101378    Answers: 2   Comments: 1

∫_(1/e) ^(tanx) (t/(1+t^2 ))dt + ∫_(1/e) ^(cotx) (1/(t(1+t^2 )))dt

$$\int_{\frac{\mathrm{1}}{{e}}} ^{{tanx}} \frac{{t}}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:+\:\int_{\frac{\mathrm{1}}{{e}}} ^{{cotx}} \frac{\mathrm{1}}{{t}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{dt} \\ $$

Question Number 101375    Answers: 1   Comments: 4

Question Number 101373    Answers: 0   Comments: 1

lim_(n→∞ ) Σ_(r=1) ^(4n) ((√n)/((√r)(3(√r)+4(√n))^2 ))

$$\underset{{n}\rightarrow\infty\:} {\mathrm{lim}}\underset{{r}=\mathrm{1}} {\overset{\mathrm{4}{n}} {\sum}}\frac{\sqrt{{n}}}{\sqrt{{r}}\left(\mathrm{3}\sqrt{{r}}+\mathrm{4}\sqrt{{n}}\right)^{\mathrm{2}} } \\ $$

Question Number 101366    Answers: 1   Comments: 2

lim_(x→0) ((x^3 −sin^3 x)/x^5 ) =?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{3}} −\mathrm{sin}\:^{\mathrm{3}} {x}}{{x}^{\mathrm{5}} }\:=? \\ $$

Question Number 101363    Answers: 1   Comments: 0

The solution set of inequality (((√((3x−7)^2 ))−2)/(x−3)) ≤ ((3−(√x^2 ))/(x−3)) is __ (A) (−∞, (1/2)] (D) [(1/2), ∞) (B) [(1/2),1 ] (E) (−∞,(2/3)] (C) (−∞,1 ]

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\mathrm{inequality} \\ $$$$\frac{\sqrt{\left(\mathrm{3x}−\mathrm{7}\right)^{\mathrm{2}} }−\mathrm{2}}{\mathrm{x}−\mathrm{3}}\:\leqslant\:\frac{\mathrm{3}−\sqrt{\mathrm{x}^{\mathrm{2}} }}{\mathrm{x}−\mathrm{3}}\:\mathrm{is}\:\_\_ \\ $$$$\left(\mathrm{A}\right)\:\left(−\infty,\:\frac{\mathrm{1}}{\mathrm{2}}\right]\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\left[\frac{\mathrm{1}}{\mathrm{2}},\:\infty\right) \\ $$$$\left(\mathrm{B}\right)\:\left[\frac{\mathrm{1}}{\mathrm{2}},\mathrm{1}\:\right]\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{E}\right)\:\left(−\infty,\frac{\mathrm{2}}{\mathrm{3}}\right] \\ $$$$\left(\mathrm{C}\right)\:\left(−\infty,\mathrm{1}\:\right]\: \\ $$

Question Number 101362    Answers: 0   Comments: 1

Question Number 101360    Answers: 0   Comments: 0

xy′=y(ylnx+1)

$${xy}'={y}\left({ylnx}+\mathrm{1}\right) \\ $$

Question Number 101350    Answers: 1   Comments: 0

Question Number 101345    Answers: 0   Comments: 3

(1)∫ ((sec^4 x tan x)/(sec^4 x+4)) dx= (2) ∫x^(2x) (2lnx +2) dx = (3) ∫_0 ^1 (√(1−x^2 )) dx =

$$\left(\mathrm{1}\right)\int\:\frac{\mathrm{sec}\:^{\mathrm{4}} {x}\:\mathrm{tan}\:{x}}{\mathrm{sec}\:^{\mathrm{4}} {x}+\mathrm{4}}\:{dx}= \\ $$$$\left(\mathrm{2}\right)\:\int{x}^{\mathrm{2}{x}} \left(\mathrm{2ln}{x}\:+\mathrm{2}\right)\:{dx}\:= \\ $$$$\left(\mathrm{3}\right)\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:{dx}\:=\: \\ $$

Question Number 101342    Answers: 1   Comments: 0

find U_n =∫_0 ^1 ((x^(2n) −1)/(lnx))dx with n integr natural and n≥2 find nature of the serie Σ U_n

$$\mathrm{find}\:\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{x}^{\mathrm{2n}} −\mathrm{1}}{\mathrm{lnx}}\mathrm{dx}\:\:\mathrm{with}\:\mathrm{n}\:\mathrm{integr}\:\mathrm{natural}\:\mathrm{and}\:\mathrm{n}\geqslant\mathrm{2} \\ $$$$\mathrm{find}\:\mathrm{nature}\:\mathrm{of}\:\mathrm{the}\:\mathrm{serie}\:\Sigma\:\mathrm{U}_{\mathrm{n}} \\ $$

Question Number 101402    Answers: 0   Comments: 3

I desire the developmenter of this apps improve adding some other functions like as:choose whole text by tap in text or choose some line at one time has many colours more

$$\mathrm{I}\:\mathrm{desire}\:\mathrm{the}\:\mathrm{developmenter}\:\mathrm{of}\:\mathrm{this}\:\mathrm{apps} \\ $$$$\mathrm{improve}\:\mathrm{adding}\:\mathrm{some}\:\mathrm{other}\:\mathrm{functions} \\ $$$$\mathrm{like}\:\mathrm{as}:\mathrm{choose}\:\mathrm{whole}\:\mathrm{text}\:\mathrm{by}\:\mathrm{tap}\:\mathrm{in} \\ $$$$\mathrm{text}\:\mathrm{or}\:\mathrm{choose}\:\mathrm{some}\:\mathrm{line}\:\mathrm{at}\:\mathrm{one}\:\mathrm{time} \\ $$$$\mathrm{has}\:\mathrm{many}\:\mathrm{colours}\:\mathrm{more} \\ $$

Question Number 101330    Answers: 0   Comments: 5

Evaluate. ∫_(−π) ^π x^9 cos x dx

$${Evaluate}. \\ $$$$\int_{−\pi} ^{\pi} {x}^{\mathrm{9}} \mathrm{cos}\:{x}\:{dx} \\ $$

Question Number 101329    Answers: 1   Comments: 0

Question Number 101328    Answers: 0   Comments: 1

this i a beautifull old question in the forum by sir.Ali Esam i Reposted it trying to find any idea to solve I=∫_(−1) ^1 (((sin(x))/(sinh^(−1) (x))))(((sin^(−1) (x))/(sinh(x))))dx i solved it numerical the value is 2.03383

$${this}\:{i}\:{a}\:{beautifull}\:{old}\:{question}\:{in}\:{the}\:{forum} \\ $$$${by}\:{sir}.{Ali}\:{Esam}\:{i}\:{Reposted}\:{it}\:{trying}\:{to} \\ $$$${find}\:{any}\:{idea}\:{to}\:{solve} \\ $$$$ \\ $$$${I}=\int_{−\mathrm{1}} ^{\mathrm{1}} \left(\frac{{sin}\left({x}\right)}{{sinh}^{−\mathrm{1}} \left({x}\right)}\right)\left(\frac{{sin}^{−\mathrm{1}} \left({x}\right)}{{sinh}\left({x}\right)}\right){dx} \\ $$$$ \\ $$$${i}\:{solved}\:{it}\:{numerical}\: \\ $$$${the}\:{value}\:{is}\:\mathrm{2}.\mathrm{03383} \\ $$

Question Number 101319    Answers: 1   Comments: 4

find the area bounded the parabola y=4x^2 and y=8−4x^2 ? by using intigral? help me

$${find}\:{the}\:{area}\:{bounded}\:{the}\:{parabola}\: \\ $$$${y}=\mathrm{4}{x}^{\mathrm{2}} \:\:\:{and}\:\:{y}=\mathrm{8}−\mathrm{4}{x}^{\mathrm{2}} \:\:?\:\:{by}\:{using}\:{intigral}? \\ $$$${help}\:{me} \\ $$

Question Number 101273    Answers: 0   Comments: 0

caoculate lim_(x→0) ((sh(sin(2x))−sin(sh(2x)))/x^3 )

$$\mathrm{caoculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\:\:\frac{\mathrm{sh}\left(\mathrm{sin}\left(\mathrm{2x}\right)\right)−\mathrm{sin}\left(\mathrm{sh}\left(\mathrm{2x}\right)\right)}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 101272    Answers: 1   Comments: 2

∫(√(sec x)) dx

$$\int\sqrt{\mathrm{sec}\:{x}}\:{dx}\: \\ $$

Question Number 101271    Answers: 0   Comments: 2

find ∫ ((xdx)/((√(x^2 +x+1))+(√(x^2 −x+1))))

$$\mathrm{find}\:\int\:\:\:\frac{\mathrm{xdx}}{\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}}} \\ $$

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