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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

$$. \\ $$

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

Question Number 103119 Answers: 0 Comments: 0

∫((log(((1+(√5))/2)(√x)−1))/(x^(√x) log(((1+(√5))/2)(√x)+1)−1))

$$\int\frac{{log}\left(\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\sqrt{{x}}−\mathrm{1}\right)}{{x}^{\sqrt{{x}}} {log}\left(\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\sqrt{{x}}+\mathrm{1}\right)−\mathrm{1}} \\ $$

Question Number 103114 Answers: 1 Comments: 2

Question Number 103143 Answers: 1 Comments: 1

Question Number 103094 Answers: 0 Comments: 4

$$. \\ $$

Question Number 103089 Answers: 1 Comments: 0

solve: (sin^2 (x)−y)dx−tan(x)dy=0

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

Question Number 103080 Answers: 0 Comments: 0

calculate A_n =∫_0 ^∞ ((cos(nx))/((1+x^2 )^n ))dx with n integr natural

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({nx}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }{dx} \\ $$$${with}\:{n}\:{integr}\:{natural} \\ $$

Question Number 103078 Answers: 0 Comments: 0

calculate ∫_(−∞) ^∞ ((xsin(2x))/((x^2 +x+1)^2 ))dx

$${calculate}\:\int_{−\infty} ^{\infty} \:\frac{{xsin}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 103077 Answers: 0 Comments: 0

find ∫_0 ^∞ ((x^2 cosx)/((x^2 +x+2)^2 ))dx

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{\mathrm{2}} {cosx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{2}\right)^{\mathrm{2}} }{dx} \\ $$

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