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Question Number 129376 Answers: 0 Comments: 1
$$\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{−{x}^{\mathrm{2}} } {dx}=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{7}+\frac{\mathrm{10}^{\mathrm{2}} }{\mathrm{32}+\frac{\mathrm{42}^{\mathrm{2}} }{\mathrm{174}+\frac{\mathrm{216}^{\mathrm{2}} }{\mathrm{1196}+\frac{\mathrm{1312}^{\mathrm{2}} }{....}}}}}}} \\ $$
Question Number 129367 Answers: 1 Comments: 1
Question Number 129345 Answers: 0 Comments: 0
$$\frac{\mathrm{1}}{\left({s}^{\mathrm{2}} +\mathrm{2}{s}+\mathrm{5}\right)^{\mathrm{2}} }\:{find}\:{inverse}\:{laplace} \\ $$
Question Number 129337 Answers: 0 Comments: 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
$${tcos}^{\mathrm{3}} {t}\:{find}\:{laplace}\:{transform}? \\ $$
Question Number 129292 Answers: 1 Comments: 1
$$\mathrm{Q}\:\mathrm{129271}\:\mathrm{please}\:\mathrm{answer} \\ $$
Question Number 129268 Answers: 1 Comments: 0
Question Number 129241 Answers: 1 Comments: 0
$$\frac{{e}^{−\pi{s}} }{{s}^{\mathrm{2}} \left({s}^{\mathrm{2}} +\mathrm{1}\right)}\:{find}\:{inverse}\:{laplace} \\ $$
Question Number 129185 Answers: 0 Comments: 2
$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{dx}}{\:\sqrt{\mathrm{97}+{sin}^{\mathrm{2}} {x}}}\:\:{Hypergeometric}\:{form} \\ $$
Question Number 129145 Answers: 0 Comments: 1
$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}^{\mathrm{2}} }{\mathrm{1}+\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{1}+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{1}+\frac{\mathrm{4}^{\mathrm{2}} }{\mathrm{1}+\frac{\mathrm{5}^{\mathrm{2}} }{\mathrm{1}+...}}}}}} \\ $$
Question Number 129132 Answers: 1 Comments: 0
Question Number 129047 Answers: 1 Comments: 0
$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2}.\mathrm{1}!}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} .\mathrm{2}!}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} .\mathrm{3}!}\right)^{\mathrm{2}} +...=\frac{\sqrt{\pi}}{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\right)} \\ $$
Question Number 129018 Answers: 1 Comments: 0
$$\frac{\left(\sqrt{{s}}−\mathrm{1}\right)^{\mathrm{2}} }{{s}^{\mathrm{2}} }\:{find}\:{the}\:{inverse}\:{laplace}\:{transformtion} \\ $$
Question Number 129010 Answers: 1 Comments: 1
Question Number 128931 Answers: 0 Comments: 2
$${Approximate} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\sqrt{{n}}}{{n}^{\mathrm{2}} +\mathrm{1}} \\ $$
Question Number 128893 Answers: 1 Comments: 0
Question Number 128845 Answers: 1 Comments: 0
$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}.\frac{\mathrm{1}.\mathrm{4}}{\left(\mathrm{5}.\mathrm{1}!\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}}.\frac{\mathrm{1}.\mathrm{4}.\mathrm{6}.\mathrm{9}}{\left(\mathrm{5}^{\mathrm{2}} .\mathrm{2}!\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{4}}.\frac{\mathrm{1}.\mathrm{4}.\mathrm{6}.\mathrm{9}.\mathrm{11}.\mathrm{14}}{\left(\mathrm{5}^{\mathrm{3}} .\mathrm{3}!\right)^{\mathrm{2}} }+...=\frac{{b}^{\mathrm{2}} \sqrt{\frac{{b}−\sqrt{{b}}}{\mathrm{2}}}}{{a}\pi} \\ $$$${Find}\:\mathrm{5}{a}−\mathrm{8}{b} \\ $$
Question Number 128731 Answers: 0 Comments: 2
$$\mathrm{for}\:\:\mathrm{a}>\mathrm{b}>\mathrm{0}\:\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{b}<\frac{\mathrm{ax}^{\mathrm{x}} +\mathrm{bx}^{−\mathrm{x}} }{\mathrm{e}^{\mathrm{x}} +\mathrm{e}^{−\mathrm{x}} }<\mathrm{a} \\ $$
Question Number 128725 Answers: 0 Comments: 0
$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{coth}\left({n}\pi\right)}{{n}^{\mathrm{4}} } \\ $$
Question Number 128561 Answers: 1 Comments: 0
Question Number 128566 Answers: 0 Comments: 1
$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2}}.\frac{\mathrm{1}}{\mathrm{1}!}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{3}}\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} }.\frac{\mathrm{1}}{\mathrm{2}!}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} }.\frac{\mathrm{1}}{\mathrm{3}!}\right)^{\mathrm{2}} +...=_{\mathrm{2}} {F}_{\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}};\mathrm{2};\mathrm{1}\right)=\frac{\mathrm{4}}{\pi} \\ $$
Question Number 128557 Answers: 1 Comments: 0
$$\: \: \: \: \: \: \: \: \: \\ $$$$\: \: \: \\ $$
Question Number 128522 Answers: 0 Comments: 0
$${f}\left({t}\right)={t}+\mathrm{1}\:\:\:\:\:\:\mathrm{0}\leqslant{t}\leqslant\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\mathrm{3}\:\:\:\:\:\:\:\:\:\:{t}>\mathrm{2} \\ $$$${find}\:{laplace}\:{transformation}? \\ $$
Question Number 128485 Answers: 1 Comments: 0
$${f}\left({t}\right)=\frac{\mathrm{1}−{cos}\mathrm{2}{t}}{{t}} \\ $$$${find}\:{laplace}\:{transformation}? \\ $$
Question Number 128460 Answers: 2 Comments: 0
$$\mathrm{2}{e}^{\mathrm{3}{t}} {sin}\mathrm{4}{t}\: \\ $$$${find}\:{laplace}\:{transformation}? \\ $$
Question Number 128445 Answers: 0 Comments: 0
$${tsinh}\mathrm{2}{t}\:{sin}\mathrm{3}{t}\: \\ $$$${find}\:{the}\:{laplace}\:{transformation}? \\ $$
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