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Question Number 102572    Answers: 0   Comments: 6

App updates: Version 2.094 has been uploaded to playstore: Enhancements: • paste plain text • Auto wrapping of lines (settings) • New construct as shown below. strike thru underline underbrace font size for selected text page breaks to split images These new constructs are disabled while posting in forum to allow all users time to update app Any issues you can report by email, telegram or as a comment to this post.

$$\mathrm{App}\:\mathrm{updates}:\: \\ $$$$\mathrm{Version}\:\mathrm{2}.\mathrm{094}\:\mathrm{has}\:\mathrm{been}\:\mathrm{uploaded} \\ $$$$\mathrm{to}\:\mathrm{playstore}: \\ $$$$\mathrm{Enhancements}: \\ $$$$\bullet\:\mathrm{paste}\:\mathrm{plain}\:\mathrm{text} \\ $$$$\bullet\:\mathrm{Auto}\:\mathrm{wrapping}\:\mathrm{of}\:\mathrm{lines}\:\left(\mathrm{settings}\right) \\ $$$$\bullet\:\mathrm{New}\:\mathrm{construct}\:\mathrm{as}\:\mathrm{shown}\:\mathrm{below}. \\ $$$$\:\:\:\:\mathrm{strike}\:\mathrm{thru} \\ $$$$\:\:\:\:\mathrm{underline} \\ $$$$\:\:\:\:\mathrm{underbrace} \\ $$$$\:\:\:\:\mathrm{font}\:\mathrm{size}\:\mathrm{for}\:\mathrm{selected}\:\mathrm{text} \\ $$$$\:\:\:\:\mathrm{page}\:\mathrm{breaks}\:\mathrm{to}\:\mathrm{split}\:\mathrm{images} \\ $$$$\:\:\:\:\mathrm{These}\:\mathrm{new}\:\mathrm{constructs}\:\mathrm{are}\:\mathrm{disabled} \\ $$$$\:\:\:\:\mathrm{while}\:\mathrm{posting}\:\mathrm{in}\:\mathrm{forum}\:\mathrm{to}\:\mathrm{allow}\:\mathrm{all} \\ $$$$\:\:\:\:\mathrm{users}\:\mathrm{time}\:\mathrm{to}\:\mathrm{update}\:\mathrm{app} \\ $$$$\mathrm{Any}\:\mathrm{issues}\:\mathrm{you}\:\mathrm{can}\:\mathrm{report}\:\mathrm{by}\:\mathrm{email}, \\ $$$$\mathrm{telegram}\:\mathrm{or}\:\mathrm{as}\:\mathrm{a}\:\mathrm{comment}\:\mathrm{to}\:\mathrm{this} \\ $$$$\mathrm{post}. \\ $$

Question Number 102553    Answers: 1   Comments: 3

Question Number 102551    Answers: 0   Comments: 0

Question Number 102549    Answers: 0   Comments: 0

let A=[1,46] show that for any p∈A we have q∈Z such as p×q≡1[47] please i need your help

$$ \\ $$$$\boldsymbol{{let}}\:\boldsymbol{{A}}=\left[\mathrm{1},\mathrm{46}\right]\: \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{for}}\:\boldsymbol{{any}}\:\boldsymbol{{p}}\in\boldsymbol{{A}}\:{we}\:\boldsymbol{{have}}\:\boldsymbol{{q}}\in\mathbb{Z} \\ $$$$\boldsymbol{{such}}\:\boldsymbol{{as}}\:\boldsymbol{{p}}×\boldsymbol{{q}}\equiv\mathrm{1}\left[\mathrm{47}\right] \\ $$$$\boldsymbol{{pleas}}{e}\:{i}\:\boldsymbol{{need}}\:\boldsymbol{{your}}\:\boldsymbol{{help}} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 102548    Answers: 0   Comments: 0

if n is a real number,find the least possible number of n,if n^2 −3n+(√(n−3)) −(√(n+3))

$${if}\:{n}\:{is}\:{a}\:{real}\:{number},{find}\:{the}\:{least}\:{possible}\:{number}\:{of}\:{n},{if} \\ $$$${n}^{\mathrm{2}} −\mathrm{3}{n}+\sqrt{{n}−\mathrm{3}}\:−\sqrt{{n}+\mathrm{3}} \\ $$

Question Number 102545    Answers: 1   Comments: 0

Question Number 102544    Answers: 2   Comments: 0

Question Number 102539    Answers: 3   Comments: 2

2+3.3+4.3^2 +5.3^2 +.....up to n terms

$$\mathrm{2}+\mathrm{3}.\mathrm{3}+\mathrm{4}.\mathrm{3}^{\mathrm{2}} +\mathrm{5}.\mathrm{3}^{\mathrm{2}} +.....{up}\:{to}\:{n}\:{terms} \\ $$

Question Number 102530    Answers: 0   Comments: 1

Question Number 102527    Answers: 3   Comments: 0

2y′′−y′+y = cos 3x

$$\mathrm{2}{y}''−{y}'+{y}\:=\:\mathrm{cos}\:\mathrm{3}{x}\: \\ $$

Question Number 102524    Answers: 1   Comments: 1

Question Number 102517    Answers: 0   Comments: 1

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

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

Question Number 102515    Answers: 2   Comments: 0

((x/y))y′= ((2y^2 +1)/(x+1))

$$\left(\frac{{x}}{{y}}\right){y}'=\:\frac{\mathrm{2}{y}^{\mathrm{2}} +\mathrm{1}}{{x}+\mathrm{1}} \\ $$

Question Number 102510    Answers: 2   Comments: 0

lim_(△x→0) ((sin^2 ((1/3)x+(1/3)△x)−sin^2 (1/3)x)/(△x))=?

$${li}\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {{m}}\frac{{sin}^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{3}}{x}+\frac{\mathrm{1}}{\mathrm{3}}\bigtriangleup{x}\right)−{sin}^{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{3}}{x}}{\bigtriangleup{x}}=? \\ $$

Question Number 102508    Answers: 0   Comments: 5

lim_(△x→0) ((e^(sin(x−△x)) −e^(sinx) )/(△x))=?

$${li}\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {{m}}\frac{{e}^{{sin}\left({x}−\bigtriangleup{x}\right)} −{e}^{{sinx}} }{\bigtriangleup{x}}=? \\ $$

Question Number 102507    Answers: 0   Comments: 2

lim_(x→e^(lnx) ) ((x/e^(lnx) ))^(−logx) =?

$${li}\underset{{x}\rightarrow{e}^{{lnx}} } {{m}}\left(\frac{{x}}{{e}^{{lnx}} }\right)^{−{logx}} =? \\ $$

Question Number 102491    Answers: 0   Comments: 0

Lets p ∈N and n∈N^∗ A_n =2^n +p and d_n =PGCD(A_n ,A_(n+1) ) 1) show that d_n /2^n 2)determine the parity of A_n as a function of that of p 3)determine the parity of d_n as a function of that of p 4)deduce pgcd(2^(2009) +2009,2^(2010) +2009)

$$ \\ $$$$\boldsymbol{{L}}{e}\boldsymbol{{ts}}\:\boldsymbol{{p}}\:\in\mathbb{N}\:\boldsymbol{{and}}\:\boldsymbol{{n}}\in\mathbb{N}^{\ast} \\ $$$$\boldsymbol{{A}}_{{n}} =\mathrm{2}^{\boldsymbol{{n}}} +\boldsymbol{{p}}\:\boldsymbol{{and}}\:\boldsymbol{{d}}_{\boldsymbol{{n}}} =\boldsymbol{{P}}{GCD}\left(\boldsymbol{{A}}_{{n}} ,\boldsymbol{{A}}_{\boldsymbol{{n}}+\mathrm{1}} \right) \\ $$$$\left.\mathrm{1}\right)\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\:\boldsymbol{{d}}_{\boldsymbol{{n}}} /\mathrm{2}^{\boldsymbol{{n}}} \\ $$$$\left.\mathrm{2}\right)\boldsymbol{{determine}}\:\boldsymbol{{the}}\:\boldsymbol{{parity}}\:{of}\:\boldsymbol{{A}}_{{n}} \:{as}\:{a}\:{function}\:{of}\:{that}\:\boldsymbol{{of}}\:\boldsymbol{{p}} \\ $$$$\left.\mathrm{3}\right){determine}\:{the}\:{parity}\:{of}\:\boldsymbol{{d}}_{\boldsymbol{{n}}} \:{as}\:{a}\:{function}\:{of}\:{that}\:{of}\:\boldsymbol{{p}} \\ $$$$\left.\mathrm{4}\right){deduce}\:{pgcd}\left(\mathrm{2}^{\mathrm{2009}} +\mathrm{2009},\mathrm{2}^{\mathrm{2010}} +\mathrm{2009}\right) \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 102490    Answers: 1   Comments: 0

x^3 −bx−c=0 ; b, c >0 ; ((b/3))^3 >((c/2))^2 To find the three real roots without the use of trigonometric solution to cubic polynomial...

$${x}^{\mathrm{3}} −{bx}−{c}=\mathrm{0}\:\:\:\:\:;\:\:{b},\:{c}\:>\mathrm{0}\:;\:\:\left(\frac{{b}}{\mathrm{3}}\right)^{\mathrm{3}} >\left(\frac{{c}}{\mathrm{2}}\right)^{\mathrm{2}} \\ $$$${To}\:{find}\:{the}\:{three}\:{real}\:{roots}\:{without} \\ $$$${the}\:{use}\:{of}\:{trigonometric}\:{solution} \\ $$$${to}\:{cubic}\:{polynomial}... \\ $$

Question Number 102484    Answers: 1   Comments: 0

Question Number 102480    Answers: 1   Comments: 0

n positive integer. when dividen by 7 give remainder 4 and when divided by 4 give remainder 2. find the value of n

$${n}\:{positive}\:{integer}.\:{when} \\ $$$${dividen}\:{by}\:\mathrm{7}\:{give}\:{remainder}\:\mathrm{4} \\ $$$${and}\:{when}\:{divided}\:{by}\:\mathrm{4}\:{give} \\ $$$${remainder}\:\mathrm{2}.\:{find}\:{the}\:{value} \\ $$$${of}\:{n}\: \\ $$

Question Number 102474    Answers: 1   Comments: 0

Un=(1+(√2))^n show that we have p_n ∈N / U_n =(√p_n )+(√(p_n +1))

$$\boldsymbol{{U}}{n}=\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)^{{n}} \\ $$$${show}\:{that}\:{we}\:{have}\:\boldsymbol{{p}}_{\boldsymbol{{n}}} \in\mathbb{N}\:/ \\ $$$$\boldsymbol{{U}}_{\boldsymbol{{n}}} =\sqrt{{p}_{{n}} }+\sqrt{{p}_{{n}} +\mathrm{1}} \\ $$

Question Number 102470    Answers: 1   Comments: 0

∫(dx/(x^(10) +x^2 ))

$$\int\frac{{dx}}{{x}^{\mathrm{10}} +{x}^{\mathrm{2}} } \\ $$$$ \\ $$

Question Number 102467    Answers: 1   Comments: 5

hello friends, is zero an even or odd number or not both?

$${hello}\:{friends},\:{is}\:{zero}\:{an}\: \\ $$$${even}\:{or}\:{odd}\:{number}\:{or}\:{not}\: \\ $$$${both}? \\ $$

Question Number 102462    Answers: 8   Comments: 0

Calculate ; J=∫(dx/(x(x^2 +x−1)^2 )) K=∫((x^3 +x−1)/((x^2 +2)^2 ))dx L=∫(dx/(x+(√(x^2 +1))))

$$\mathrm{Calculate}\:; \\ $$$$\mathrm{J}=\int\frac{\mathrm{dx}}{\mathrm{x}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\mathrm{K}=\int\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{x}−\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$$$\mathrm{L}=\int\frac{\mathrm{dx}}{\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}} \\ $$

Question Number 102461    Answers: 1   Comments: 0

∫ (dx/(√(5e^(2x) +4e^x +1))) =?

$$\int\:\frac{{dx}}{\sqrt{\mathrm{5}{e}^{\mathrm{2}{x}} +\mathrm{4}{e}^{{x}} +\mathrm{1}}}\:=? \\ $$

Question Number 102555    Answers: 0   Comments: 0

∫_0 ^1 ((x^(98) −99x+98)/(logx))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{98}} −\mathrm{99}{x}+\mathrm{98}}{{logx}}{dx} \\ $$

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