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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

Question Number 91211 Answers: 1 Comments: 1

x dy +5y dx = 2y^4 x dx

$${x}\:{dy}\:+\mathrm{5}{y}\:{dx}\:=\:\mathrm{2}{y}^{\mathrm{4}} {x}\:{dx} \\ $$

Question Number 91196 Answers: 1 Comments: 1

Question Number 91195 Answers: 1 Comments: 0

what is the duble fictorial furmolla?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{duble}\:\mathrm{fictorial}\:\mathrm{furmolla}? \\ $$

Question Number 91185 Answers: 1 Comments: 2

f(x)=(x−3)^5 ln(1+x) f^((2020)) (3)=?

$${f}\left({x}\right)=\left({x}−\mathrm{3}\right)^{\mathrm{5}} {ln}\left(\mathrm{1}+{x}\right) \\ $$$${f}^{\left(\mathrm{2020}\right)} \left(\mathrm{3}\right)=? \\ $$

Question Number 91183 Answers: 0 Comments: 0

Question Number 91182 Answers: 1 Comments: 0

lim_(x→0) ((2x^6 +3x^2 −3tan^2 x)/(3x^6 ))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}{x}^{\mathrm{6}} +\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3tan}\:^{\mathrm{2}} {x}}{\mathrm{3}{x}^{\mathrm{6}} } \\ $$

Question Number 91178 Answers: 0 Comments: 2

Question Number 91176 Answers: 0 Comments: 1

My Post Filter Issue Dear Mr W, can you send a few screenshots on what is seen when using filter myposts. Thank You

$$\mathrm{My}\:\mathrm{Post}\:\mathrm{Filter}\:\mathrm{Issue} \\ $$$$\mathrm{Dear}\:\mathrm{Mr}\:\mathrm{W},\:\mathrm{can}\:\mathrm{you}\:\mathrm{send}\:\mathrm{a}\:\mathrm{few}\:\mathrm{screenshots} \\ $$$$\mathrm{on}\:\mathrm{what}\:\mathrm{is}\:\mathrm{seen}\:\mathrm{when}\:\mathrm{using}\:\mathrm{filter} \\ $$$$\mathrm{myposts}.\:\mathrm{Thank}\:\mathrm{You} \\ $$

Question Number 91177 Answers: 1 Comments: 1

6^((log_2 x)^2 ) + x^((log_2 x)) = 12

$$\mathrm{6}^{\left(\mathrm{log}_{\mathrm{2}} \:{x}\right)^{\mathrm{2}} } \:+\:{x}^{\left(\mathrm{log}_{\mathrm{2}} \:{x}\right)} \:=\:\mathrm{12}\: \\ $$

Question Number 91167 Answers: 1 Comments: 4

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