Question Number 135103 by frc2crc last updated on 10/Mar/21 $${f}\left({x}\right)=\mathrm{1}+\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−{x}\right)^{{n}} }{{n}} \\ $$ Commented by Dwaipayan Shikari last updated on 10/Mar/21 $$\mathrm{1}−\left(−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{{x}^{\mathrm{3}}…
Question Number 69564 by mathmax by abdo last updated on 25/Sep/19 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} \:+{a}}\:\:\:{with}\:{a}\:{real}\:{and}\:{a}>\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:\:{calculate}\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +{a}\right)^{\mathrm{2}} }…
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Question Number 4027 by Rasheed Soomro last updated on 27/Dec/15 $${Let}\:\mathbb{A}\:{denotes}\:{the}\:{Set}\:{of}\:{Algebraic}\:{Numbers} \\ $$$${and}\:\:\mathbb{T}\:\:\:{the}\:{Set}\:{of}\:{Trancedental}\:{Numbers}. \\ $$$${Discuss}\:{the}\:{following}: \\ $$$$\bullet{Are}\:\mathbb{A}\:{and}\:\mathbb{T}\:\:\boldsymbol{{closed}}\:{with}\:{respect}\:{to}\:\: \\ $$$$\boldsymbol{{addition}}\:{and}\:\boldsymbol{{multiplication}}\:? \\ $$$$\bullet{Are}\:\mathbb{A}−\left\{\mathrm{0}\right)\:\:{and}\:\mathbb{T}\:\:\boldsymbol{{closed}}\:{with}\:{respect}\:{to}\:\: \\ $$$$\boldsymbol{{division}}? \\ $$…
Question Number 69563 by mathmax by abdo last updated on 25/Sep/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} \:+\mathrm{1}} \\ $$ Commented by mathmax by abdo last updated…
Question Number 135099 by 0731619177 last updated on 10/Mar/21 Answered by Dwaipayan Shikari last updated on 10/Mar/21 $${I}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \frac{{f}\left({ax}\right)−{f}\left({bx}\right)}{{x}}{dx} \\ $$$${I}'\left({a}\right)=\int_{\mathrm{0}} ^{\infty} {f}'\left({ax}\right){dx}=\frac{\mathrm{1}}{{a}}\underset{{z}\rightarrow\infty} {\mathrm{lim}}\left({f}\left({z}\right)−{f}\left(\mathrm{0}\right)\right)…
Question Number 4025 by 123456 last updated on 26/Dec/15 $${f}_{{n}+\mathrm{1}} \left({x}\right)={x}^{{f}_{{n}} \left({x}\right)} \\ $$$${g}_{{n}+\mathrm{1}} \left({x}\right)=\left[{g}_{{n}} \left({x}\right)\right]^{{x}} \\ $$$${h}_{{n}+\mathrm{1}} \left({x}\right)=\left[{h}_{{n}} \left({x}\right)\right]^{{h}_{{n}} \left({x}\right)} \\ $$$${f}_{\mathrm{0}} \left({x}\right)={g}_{\mathrm{0}} \left({x}\right)={h}_{\mathrm{0}}…
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Question Number 69557 by aliesam last updated on 24/Sep/19 Answered by MJS last updated on 24/Sep/19 $${x}=\mathrm{72} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 135091 by mohammad17 last updated on 10/Mar/21 $${find} \\ $$$$\left(\mathrm{1}\right)\int_{{C}} {ZImZ}^{\mathrm{2}} {dz}\:\:{if}\:{C}=\left\{\mid{Z}\mid=\mathrm{1}:−\pi\leqslant\theta\leqslant\mathrm{0}\right\} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\int_{{C}} \frac{{dz}}{{Z}^{\mathrm{4}} +\mathrm{1}}\:\:\:{if}\:{C}=\mid{z}−\mathrm{1}+\mathrm{2}{i}\mid=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$ \\ $$$${help}\:{me}\:{sir} \\…