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Question Number 91321 Answers: 0 Comments: 3

1)find eigen values and corresponding eigen vector of the matrix A= [((cos(θ)),(−sin(θ))),((sin(θ)),( cos(θ))) ] 2)solve 6y^2 dx−x(y+2x^2 )dy=0

$$\left.\mathrm{1}\right){find}\:{eigen}\:{values}\:{and}\:{corresponding} \\ $$$${eigen}\:{vector}\:{of}\:{the}\:{matrix} \\ $$$$ \\ $$$${A}=\begin{bmatrix}{{cos}\left(\theta\right)}&{−{sin}\left(\theta\right)}\\{{sin}\left(\theta\right)}&{\:\:\:\:\:{cos}\left(\theta\right)}\end{bmatrix} \\ $$$$ \\ $$$$\left.\mathrm{2}\right){solve} \\ $$$$ \\ $$$$\mathrm{6}{y}^{\mathrm{2}} {dx}−{x}\left({y}+\mathrm{2}{x}^{\mathrm{2}} \right){dy}=\mathrm{0} \\ $$

Question Number 91310 Answers: 0 Comments: 0

show that ∫_0 ^(π/2) cot (x) ln(sec(x)) dx=(π^2 /(24))

$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {cot}\:\left({x}\right)\:{ln}\left({sec}\left({x}\right)\right)\:{dx}=\frac{\pi^{\mathrm{2}} }{\mathrm{24}} \\ $$

Question Number 91308 Answers: 0 Comments: 2

∫ (x^2 /(x^4 −x^2 −2)) dx ?

$$\int\:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} −\mathrm{2}}\:{dx}\:? \\ $$

Question Number 91303 Answers: 0 Comments: 3

Question Number 91302 Answers: 2 Comments: 0

Question Number 91298 Answers: 1 Comments: 1

what is the particular integral of (D^2 +6D+5)y = e^(−5x )

$${what}\:{is}\:{the}\:{particular}\:{integral} \\ $$$${of}\:\left({D}^{\mathrm{2}} +\mathrm{6}{D}+\mathrm{5}\right){y}\:=\:{e}^{−\mathrm{5}{x}\:} \: \\ $$

Question Number 91297 Answers: 0 Comments: 2

Can someone please recommend a good advanced math textbook that covers precalculus?

$${Can}\:{someone}\:{please}\:{recommend} \\ $$$${a}\:{good}\:{advanced}\:{math}\:{textbook} \\ $$$${that}\:{covers}\:{precalculus}? \\ $$

Question Number 91291 Answers: 0 Comments: 3

x dy +2y dx = 2x^3 y^2 dx

$${x}\:{dy}\:+\mathrm{2}{y}\:{dx}\:=\:\mathrm{2}{x}^{\mathrm{3}} {y}^{\mathrm{2}} \:{dx} \\ $$

Question Number 91290 Answers: 0 Comments: 1

Question Number 91287 Answers: 1 Comments: 0

y′′+2y′+5y=3sin 4t

$${y}''+\mathrm{2}{y}'+\mathrm{5}{y}=\mathrm{3sin}\:\mathrm{4}{t} \\ $$

Question Number 91277 Answers: 2 Comments: 0

p=1−(1/2)+(1/3)−(1/4)+...+(1/(2003))−(1/(2004)) q=(1/(1003))+(1/(1004))+...+(1/(2004)) p^2 +q^2 =

$${p}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}+...+\frac{\mathrm{1}}{\mathrm{2003}}−\frac{\mathrm{1}}{\mathrm{2004}} \\ $$$${q}=\frac{\mathrm{1}}{\mathrm{1003}}+\frac{\mathrm{1}}{\mathrm{1004}}+...+\frac{\mathrm{1}}{\mathrm{2004}} \\ $$$${p}^{\mathrm{2}} +{q}^{\mathrm{2}} \:=\: \\ $$

Question Number 91275 Answers: 0 Comments: 6

Question Number 91274 Answers: 0 Comments: 0

lim_(n→∞) n^(−n^2 ) [(n+1)(n+(1/2))....(n+(1/2^(n−1) ))]^n

$$\underset{{n}\rightarrow\infty} {{lim}n}^{−{n}^{\mathrm{2}} } \left[\left({n}+\mathrm{1}\right)\left({n}+\frac{\mathrm{1}}{\mathrm{2}}\right)....\left({n}+\frac{\mathrm{1}}{\mathrm{2}^{{n}−\mathrm{1}} }\right)\right]^{{n}} \\ $$

Question Number 91272 Answers: 1 Comments: 0

(D^2 +4)y = sin 2x

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

Question Number 91271 Answers: 1 Comments: 1

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

$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 91270 Answers: 0 Comments: 0

find ∫_0 ^∞ ((arctan(x+(1/x)))/(x^2 +1))dx

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}+\frac{\mathrm{1}}{{x}}\right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$

Question Number 91269 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((x^2 −1)/((x^2 +x+2)^3 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{2}\right)^{\mathrm{3}} }{dx} \\ $$

Question Number 91268 Answers: 0 Comments: 5

let A = (((1 2)),((1 −1)) ) 1) calculste A^n 2) determine e^A and e^(−2A) 3)find cos(A)and sinA is cos^2 A +sin^2 A =I? 4) determine sh(A) and ch(A) is ch^2 A−sh^2 A =I ?

$${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{1}\:\:\:\:\:−\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculste}\:{A}^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:\:{e}^{{A}} \:\:{and}\:{e}^{−\mathrm{2}{A}} \\ $$$$\left.\mathrm{3}\right){find}\:{cos}\left({A}\right){and}\:{sinA}\:\:\:{is}\:{cos}^{\mathrm{2}} {A}\:+{sin}^{\mathrm{2}} {A}\:={I}? \\ $$$$\left.\mathrm{4}\right)\:{determine}\:{sh}\left({A}\right)\:{and}\:{ch}\left({A}\right)\:\:{is}\:{ch}^{\mathrm{2}} {A}−{sh}^{\mathrm{2}} {A}\:={I}\:\:? \\ $$

Question Number 91263 Answers: 0 Comments: 0

y′′′′ +2y′′+y = sin x

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

Question Number 91258 Answers: 0 Comments: 0

prove that _2 F_1 (α,β,β−a+1,−1)=((Γ(β−a+1)Γ((β/2)+1))/(Γ(β+1)Γ((β/2)−α+1)))

$${prove}\:{that} \\ $$$$\:\:\:_{\mathrm{2}} {F}_{\mathrm{1}} \left(\alpha,\beta,\beta−{a}+\mathrm{1},−\mathrm{1}\right)=\frac{\Gamma\left(\beta−{a}+\mathrm{1}\right)\Gamma\left(\frac{\beta}{\mathrm{2}}+\mathrm{1}\right)}{\Gamma\left(\beta+\mathrm{1}\right)\Gamma\left(\frac{\beta}{\mathrm{2}}−\alpha+\mathrm{1}\right)} \\ $$

Question Number 92440 Answers: 0 Comments: 1

Question Number 91230 Answers: 2 Comments: 0

Σ_(j=o) ^m ^a C_j ^b C_(m−j) = ^(a+b) C_m solve this problem

$$\underset{{j}={o}} {\overset{{m}} {\sum}}\:\:\overset{{a}} {\:}{C}_{{j}} \:\overset{{b}} {\:}{C}_{{m}−{j}} \:\:=\:\overset{{a}+{b}} {\:}{C}_{{m}} \\ $$$${solve}\:{this}\:{problem} \\ $$

Question Number 91228 Answers: 0 Comments: 1

lim_(x→1) lnx(∫_0 ^x (dt/(lnt)) )

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\:{lnx}\left(\int_{\mathrm{0}} ^{{x}} \:\frac{{dt}}{{lnt}}\:\right)\: \\ $$

Question Number 91223 Answers: 1 Comments: 0

what is complementary error function erfc(t)?

$${what}\:{is}\:{complementary}\:{error}\:{function} \\ $$$${erfc}\left({t}\right)? \\ $$

Question Number 91220 Answers: 0 Comments: 3

∫_1 ^x ((lnt)/(1+t^2 ))dt

$$\int_{\mathrm{1}} ^{\mathrm{x}} \frac{\mathrm{lnt}}{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }\mathrm{dt} \\ $$

Question Number 91217 Answers: 0 Comments: 3

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