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Question Number 103205 Answers: 2 Comments: 0

Question Number 103203 Answers: 2 Comments: 0

y′′+4y′+4y = (e^(−2x) /x^2 )

$${y}''+\mathrm{4}{y}'+\mathrm{4}{y}\:=\:\frac{{e}^{−\mathrm{2}{x}} }{{x}^{\mathrm{2}} }\: \\ $$

Question Number 103201 Answers: 2 Comments: 1

(D^2 −2D+1)y = x ln(x)

$$\left({D}^{\mathrm{2}} −\mathrm{2}{D}+\mathrm{1}\right){y}\:=\:{x}\:\mathrm{ln}\left({x}\right) \\ $$

Question Number 103198 Answers: 4 Comments: 1

∫_0 ^1 sin(logx)dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {sin}\left({logx}\right){dx} \\ $$

Question Number 103196 Answers: 1 Comments: 0

∫_0 ^1 ((((1/2)−x) ln(1−x) dx)/(x^2 −x+1)) ?

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}−{x}\right)\:\mathrm{ln}\left(\mathrm{1}−{x}\right)\:{dx}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}\:? \\ $$

Question Number 103195 Answers: 0 Comments: 1

893x = 266 (mod 2432)

$$\mathrm{893}{x}\:=\:\mathrm{266}\:\left({mod}\:\mathrm{2432}\right) \\ $$

Question Number 103193 Answers: 0 Comments: 1

(dy/dx) + y.cot (x) = sin (x)

$$\frac{{dy}}{{dx}}\:+\:{y}.\mathrm{cot}\:\left({x}\right)\:=\:\mathrm{sin}\:\left({x}\right) \\ $$

Question Number 103190 Answers: 1 Comments: 0

∫_(π/4) ^(π/2) ln(ln(tan x)) dx

$$\underset{\pi/\mathrm{4}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{ln}\left(\mathrm{ln}\left(\mathrm{tan}\:{x}\right)\right)\:{dx}\: \\ $$

Question Number 103186 Answers: 0 Comments: 0

Discuss whether the mean value theorem applies to the function f(x)=(√(x^2 −4)) ?

$${Discuss}\:{whether}\:{the}\:{mean}\:{value}\:{theorem}\: \\ $$$${applies}\:{to}\:{the}\:{function}\:{f}\left({x}\right)=\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}\:\:? \\ $$

Question Number 103180 Answers: 0 Comments: 0

Let S be a nonempty subset of R that is bounded below . prove that (inf(S)=−sup{−s:s∈S})?

$${Let}\:{S}\:{be}\:{a}\:{nonempty}\:{subset}\:{of}\:{R}\:{that}\:{is}\:{bounded} \\ $$$${below}\:.\:{prove}\:{that}\:\left({inf}\left({S}\right)=−{sup}\left\{−{s}:{s}\in{S}\right\}\right)? \\ $$

Question Number 103179 Answers: 1 Comments: 1

Question Number 103177 Answers: 1 Comments: 0

Find the gineral form of the sequence ⟨2,−2,2,−2,.....⟩?

$${Find}\:{the}\:{gineral}\:{form}\:{of}\:{the}\:{sequence}\:\langle\mathrm{2},−\mathrm{2},\mathrm{2},−\mathrm{2},.....\rangle? \\ $$

Question Number 103171 Answers: 1 Comments: 1

Question Number 103170 Answers: 0 Comments: 3

x^x^x =3 x=?

$${x}^{{x}^{{x}} } =\mathrm{3}\:\:\:\:\:\:{x}=? \\ $$$$ \\ $$

Question Number 103168 Answers: 1 Comments: 0

The particular solution of differential equation of (dy/dx)+(y/x)=k is y=(1/x)+2x thus ,whats the value of k ?

$${The}\:{particular}\:{solution}\:{of}\:{differential}\:{equation}\: \\ $$$${of}\:\frac{{dy}}{{dx}}+\frac{{y}}{{x}}={k}\:{is}\:{y}=\frac{\mathrm{1}}{{x}}+\mathrm{2}{x}\:{thus}\:,{whats}\:{the}\:{value}\:{of}\:{k}\:? \\ $$

Question Number 103165 Answers: 0 Comments: 3

Question Number 103159 Answers: 0 Comments: 1

how do you represent the distance between M andN is 7

$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{do}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{represent}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{distance}}\:\boldsymbol{\mathrm{between}} \\ $$$$\boldsymbol{\mathrm{M}}\:{and}\boldsymbol{{N}}\:\mathrm{is}\:\mathrm{7} \\ $$

Question Number 103155 Answers: 0 Comments: 2

If cos^(−1) x+cos^(−1) y+cos^(−1) z+cos^(−1) u=2π, then x^(1999) +y^(2000) +z^(2001) +u^(2002) =

$$\mathrm{If}\:\mathrm{cos}^{−\mathrm{1}} {x}+\mathrm{cos}^{−\mathrm{1}} {y}+\mathrm{cos}^{−\mathrm{1}} {z}+\mathrm{cos}^{−\mathrm{1}} {u}=\mathrm{2}\pi, \\ $$$$\mathrm{then}\:\:{x}^{\mathrm{1999}} +{y}^{\mathrm{2000}} +{z}^{\mathrm{2001}} +{u}^{\mathrm{2002}} = \\ $$

Question Number 103154 Answers: 2 Comments: 0

∫_0 ^1 logxlog(1−x)dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {logxlog}\left(\mathrm{1}−{x}\right){dx} \\ $$

Question Number 103151 Answers: 0 Comments: 1

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Question Number 103149 Answers: 2 Comments: 0

using first principal y = ln (sin (√x)) →y′ = ?

$${using}\:{first}\:{principal}\: \\ $$$${y}\:=\:\mathrm{ln}\:\left(\mathrm{sin}\:\sqrt{{x}}\right)\:\rightarrow{y}'\:=\:? \\ $$

Question Number 103147 Answers: 2 Comments: 0

Question Number 103138 Answers: 1 Comments: 2

(D^2 −4D)y = x^2 e^(2x)

$$\left({D}^{\mathrm{2}} −\mathrm{4}{D}\right){y}\:=\:{x}^{\mathrm{2}} \:{e}^{\mathrm{2}{x}} \\ $$

Question Number 103130 Answers: 3 Comments: 1

find out the fourth member of the following formula after expansion [πx+(2/x)]^8

$$ \\ $$$${find}\:{out}\:{the}\:{fourth}\:{member}\:{of}\:{the} \\ $$$${following}\:{formula}\:{after}\:{expansion} \\ $$$$\left[\pi{x}+\frac{\mathrm{2}}{{x}}\right]^{\mathrm{8}} \\ $$

Question Number 103124 Answers: 1 Comments: 0

Li(z)=∫_2 ^z (1/(ln t))dt Li(a+ib)=R(∫_2 ^(a+ib) (1/(ln t))dt)+iI(∫_2 ^(a+ib) (1/(ln t))dt) Can you explain me how get the formula for R(Li(z)) and I(Li(z))?

$$\mathrm{Li}\left({z}\right)=\int_{\mathrm{2}} ^{{z}} \frac{\mathrm{1}}{\mathrm{ln}\:{t}}\mathrm{d}{t} \\ $$$$\mathrm{Li}\left({a}+{ib}\right)=\mathfrak{R}\left(\int_{\mathrm{2}} ^{{a}+{ib}} \frac{\mathrm{1}}{\mathrm{ln}\:{t}}\mathrm{d}{t}\right)+{i}\mathfrak{I}\left(\int_{\mathrm{2}} ^{{a}+{ib}} \frac{\mathrm{1}}{\mathrm{ln}\:{t}}\mathrm{d}{t}\right) \\ $$$$\mathrm{Can}\:\mathrm{you}\:\mathrm{explain}\:\mathrm{me} \\ $$$$\mathrm{how}\:\mathrm{get}\:\mathrm{the}\:\mathrm{formula} \\ $$$$\mathrm{for}\:\mathfrak{R}\left(\mathrm{Li}\left({z}\right)\right)\:\mathrm{and} \\ $$$$\mathfrak{I}\left(\mathrm{Li}\left({z}\right)\right)? \\ $$

Question Number 103120 Answers: 0 Comments: 0

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