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Question Number 129337 Answers: 0 Comments: 1

a set S⊂R and S={(n/( (√(n^2 +1)))): n∈N, n≥1} show that minS=(1/( (√2))) and supS=1

$$\mathrm{a}\:\mathrm{set}\:\mathrm{S}\subset\mathbb{R}\:\:\:\mathrm{and}\:\:\mathrm{S}=\left\{\frac{\mathrm{n}}{\:\sqrt{\mathrm{n}^{\mathrm{2}} +\mathrm{1}}}:\:\mathrm{n}\in\mathbb{N},\:\mathrm{n}\geqslant\mathrm{1}\right\} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{minS}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\:\mathrm{and}\:\:\mathrm{supS}=\mathrm{1} \\ $$

Question Number 129308 Answers: 1 Comments: 0

tcos^3 t find laplace transform?

$${tcos}^{\mathrm{3}} {t}\:{find}\:{laplace}\:{transform}? \\ $$

Question Number 129292 Answers: 1 Comments: 1

Q 129271 please answer

$$\mathrm{Q}\:\mathrm{129271}\:\mathrm{please}\:\mathrm{answer} \\ $$

Question Number 129268 Answers: 1 Comments: 0

(1/((s^2 +2s+5)^2 )) find inverse laplace

$$\frac{\mathrm{1}}{\left({s}^{\mathrm{2}} +\mathrm{2}{s}+\mathrm{5}\right)^{\mathrm{2}} }\:{find}\:{inverse}\:{laplace} \\ $$

Question Number 129241 Answers: 1 Comments: 0

(e^(−πs) /(s^2 (s^2 +1))) find inverse laplace

$$\frac{{e}^{−\pi{s}} }{{s}^{\mathrm{2}} \left({s}^{\mathrm{2}} +\mathrm{1}\right)}\:{find}\:{inverse}\:{laplace} \\ $$

Question Number 129185 Answers: 0 Comments: 2

∫_0 ^(π/2) (dx/( (√(97+sin^2 x)))) Hypergeometric form

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{dx}}{\:\sqrt{\mathrm{97}+{sin}^{\mathrm{2}} {x}}}\:\:{Hypergeometric}\:{form} \\ $$

Question Number 129145 Answers: 0 Comments: 1

1+(1/(1+(1^2 /(1+(2^2 /(1+(3^2 /(1+(4^2 /(1+(5^2 /(1+...))))))))))))

$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}^{\mathrm{2}} }{\mathrm{1}+\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{1}+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{1}+\frac{\mathrm{4}^{\mathrm{2}} }{\mathrm{1}+\frac{\mathrm{5}^{\mathrm{2}} }{\mathrm{1}+...}}}}}} \\ $$

Question Number 129132 Answers: 1 Comments: 0

Question Number 129047 Answers: 1 Comments: 0

1+(1/2)((1/(2.1!)))^2 +(1/2^2 )(((1.3)/(2^2 .2!)))^2 +(1/2^3 )(((1.3.5)/(2^3 .3!)))^2 +...=((√π)/(Γ^2 ((3/4))))

$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2}.\mathrm{1}!}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} .\mathrm{2}!}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} .\mathrm{3}!}\right)^{\mathrm{2}} +...=\frac{\sqrt{\pi}}{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\right)} \\ $$

Question Number 129018 Answers: 1 Comments: 0

((((√s)−1)^2 )/s^2 ) find the inverse laplace transformtion

$$\frac{\left(\sqrt{{s}}−\mathrm{1}\right)^{\mathrm{2}} }{{s}^{\mathrm{2}} }\:{find}\:{the}\:{inverse}\:{laplace}\:{transformtion} \\ $$

Question Number 129010 Answers: 1 Comments: 1

Question Number 128931 Answers: 0 Comments: 2

Approximate Σ_(n=1) ^∞ ((√n)/(n^2 +1))

$${Approximate} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\sqrt{{n}}}{{n}^{\mathrm{2}} +\mathrm{1}} \\ $$

Question Number 128893 Answers: 1 Comments: 0

Question Number 128845 Answers: 1 Comments: 0

1+(1/2).((1.4)/((5.1!)^2 ))+(1/3).((1.4.6.9)/((5^2 .2!)^2 ))+(1/4).((1.4.6.9.11.14)/((5^3 .3!)^2 ))+...=((b^2 (√((b−(√b))/2)))/(aπ)) Find 5a−8b

$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}.\frac{\mathrm{1}.\mathrm{4}}{\left(\mathrm{5}.\mathrm{1}!\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}}.\frac{\mathrm{1}.\mathrm{4}.\mathrm{6}.\mathrm{9}}{\left(\mathrm{5}^{\mathrm{2}} .\mathrm{2}!\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{4}}.\frac{\mathrm{1}.\mathrm{4}.\mathrm{6}.\mathrm{9}.\mathrm{11}.\mathrm{14}}{\left(\mathrm{5}^{\mathrm{3}} .\mathrm{3}!\right)^{\mathrm{2}} }+...=\frac{{b}^{\mathrm{2}} \sqrt{\frac{{b}−\sqrt{{b}}}{\mathrm{2}}}}{{a}\pi} \\ $$$${Find}\:\mathrm{5}{a}−\mathrm{8}{b} \\ $$

Question Number 128731 Answers: 0 Comments: 2

for a>b>0 show that b<((ax^x +bx^(−x) )/(e^x +e^(−x) ))<a

$$\mathrm{for}\:\:\mathrm{a}>\mathrm{b}>\mathrm{0}\:\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{b}<\frac{\mathrm{ax}^{\mathrm{x}} +\mathrm{bx}^{−\mathrm{x}} }{\mathrm{e}^{\mathrm{x}} +\mathrm{e}^{−\mathrm{x}} }<\mathrm{a} \\ $$

Question Number 128725 Answers: 0 Comments: 0

Σ_(n=1) ^∞ ((coth(nπ))/n^4 )

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{coth}\left({n}\pi\right)}{{n}^{\mathrm{4}} } \\ $$

Question Number 128561 Answers: 1 Comments: 0

Question Number 128566 Answers: 0 Comments: 1

1+(1/2)((1/2).(1/(1!)))^2 +(1/3)(((1.3)/2^2 ).(1/(2!)))^2 +(1/4)(((1.3.5)/2^3 ).(1/(3!)))^2 +...=_2 F_1 ((1/2),(1/2);2;1)=(4/π)

Question Number 128557 Answers: 1 Comments: 0

$$\: \: \: \: \: \: \: \: \: \\ $$$$\: \: \: \\ $$

Question Number 128522 Answers: 0 Comments: 0

f(t)=t+1 0≤t≤2 =3 t>2 find laplace transformation?

$${f}\left({t}\right)={t}+\mathrm{1}\:\:\:\:\:\:\mathrm{0}\leqslant{t}\leqslant\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\mathrm{3}\:\:\:\:\:\:\:\:\:\:{t}>\mathrm{2} \\ $$$${find}\:{laplace}\:{transformation}? \\ $$

Question Number 128485 Answers: 1 Comments: 0

f(t)=((1−cos2t)/t) find laplace transformation?

$${f}\left({t}\right)=\frac{\mathrm{1}−{cos}\mathrm{2}{t}}{{t}} \\ $$$${find}\:{laplace}\:{transformation}? \\ $$

Question Number 128460 Answers: 2 Comments: 0

2e^(3t) sin4t find laplace transformation?

$$\mathrm{2}{e}^{\mathrm{3}{t}} {sin}\mathrm{4}{t}\: \\ $$$${find}\:{laplace}\:{transformation}? \\ $$

Question Number 128445 Answers: 0 Comments: 0

tsinh2t sin3t find the laplace transformation?

$${tsinh}\mathrm{2}{t}\:{sin}\mathrm{3}{t}\: \\ $$$${find}\:{the}\:{laplace}\:{transformation}? \\ $$

Question Number 128321 Answers: 0 Comments: 1

Prove Σ_(n≥0) ^∞ (((a)_n (b)_n )/((c)_n n!))=((Γ(c)Γ(c−a−b))/(Γ(c−a)Γ(c−b))) Where (a)_n =Π_(k=0) ^(n−1) (k+a)

$${Prove} \\ $$$$\underset{{n}\geqslant\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left({a}\right)_{{n}} \left({b}\right)_{{n}} }{\left({c}\right)_{{n}} {n}!}=\frac{\Gamma\left({c}\right)\Gamma\left({c}−{a}−{b}\right)}{\Gamma\left({c}−{a}\right)\Gamma\left({c}−{b}\right)} \\ $$$${Where}\:\left({a}\right)_{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\prod}}\left({k}+{a}\right) \\ $$

Question Number 128382 Answers: 0 Comments: 1

y=x^x^2

$${y}={x}^{{x}^{\mathrm{2}} } \\ $$

Question Number 128256 Answers: 0 Comments: 6

1+(1/(2!1!))((1/2))^2 +(1/(3!2!))(((1.3)/2^2 ))^2 +(1/(4!3!))(((1.3.5)/2^3 ))^2 +....=(4/π) Prove the above Relation

$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}!\mathrm{1}!}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{3}!\mathrm{2}!}\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} }\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{4}!\mathrm{3}!}\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} }\right)^{\mathrm{2}} +....=\frac{\mathrm{4}}{\pi} \\ $$$${Prove}\:{the}\:{above}\:{Relation} \\ $$

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