Question Number 144700 by mathmax by abdo last updated on 28/Jun/21 $$\mathrm{find}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{x}^{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} } \\ $$ Answered by qaz last updated on 28/Jun/21…
Question Number 144699 by mathmax by abdo last updated on 28/Jun/21 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{log}\left(\mathrm{cht}\right) \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by Olaf_Thorendsen last updated on 28/Jun/21 $${f}\:\mathrm{is}\:\mathrm{not}\:\mathrm{periodic}\:! \\…
Question Number 13598 by Tinkutara last updated on 21/May/17 $$\mathrm{If}\:{g}\left({x}\right)\:=\:{x}^{\mathrm{2}} \:+\:{x}\:−\:\mathrm{2}\:\mathrm{and} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:{gof}\left({x}\right)\:=\:\mathrm{2}{x}^{\mathrm{2}} \:−\:\mathrm{5}{x}\:+\:\mathrm{2},\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:{f}\left({x}\right)\:=\:\mathrm{2}{x}\:−\:\mathrm{3}. \\ $$ Commented by mrW1 last updated on 21/May/17…
Question Number 13601 by Tinkutara last updated on 21/May/17 $$\mathrm{Let}\:{f}\::\:\mathbb{R}\:−\:\left\{\frac{\mathrm{3}}{\mathrm{5}}\right\}\:\rightarrow\:\mathbb{R}\:\mathrm{be}\:\mathrm{defined}\:\mathrm{by} \\ $$$${f}\left({x}\right)\:=\:\frac{\mathrm{3}{x}\:+\:\mathrm{2}}{\mathrm{5}{x}\:−\:\mathrm{3}}\:.\:\mathrm{Then}, \\ $$$$\left(\mathrm{a}\right)\:{f}^{−\mathrm{1}} \left({x}\right)\:=\:{x} \\ $$$$\left(\mathrm{b}\right)\:{f}^{−\mathrm{1}} \left({x}\right)\:=\:−{f}\left({x}\right) \\ $$$$\left(\mathrm{c}\right)\:{fof}\left({x}\right)\:=\:−{x} \\ $$$$\left(\mathrm{d}\right)\:{f}^{−\mathrm{1}} \left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{19}}{f}\left({x}\right) \\ $$…
Question Number 13595 by Tinkutara last updated on 21/May/17 $$\mathrm{If}\:{f}\::\:\mathbb{R}\:\rightarrow\:\left(−\mathrm{1},\:\mathrm{1}\right)\:\mathrm{is}\:\mathrm{defined}\:\mathrm{by} \\ $$$${f}\left({x}\right)\:=\:\frac{−{x}\mid{x}\mid}{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\:,\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)\:=\:−\mathrm{sgn}\left({x}\right)\sqrt{\frac{\mid{x}\mid}{\mathrm{1}\:−\:\mid{x}\mid}} \\ $$ Answered by mrW1 last updated on 21/May/17…
Question Number 79107 by mathmax by abdo last updated on 22/Jan/20 $${calculate}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left({x}^{\mathrm{2}} \:+\frac{{a}}{{x}^{\mathrm{2}} }\right)} {dx}\:{with}\:{a}>\mathrm{0} \\ $$ Commented by mathmax by abdo last…
Question Number 79106 by mathmax by abdo last updated on 22/Jan/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left({x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)} {dx} \\ $$ Commented by mathmax by abdo last…
Question Number 79108 by mathmax by abdo last updated on 22/Jan/20 $${decompose}\:{F}\left({x}\right)=\frac{{nx}^{{n}} }{{x}^{\mathrm{2}{n}} \:+\mathrm{1}}\:\:{inside}\:{C}\left({x}\right)\:{and}\:{R}\left({x}\right)\:\:\left({n}\geqslant\mathrm{2}\right) \\ $$$${and}\:{determine}\:\int_{\mathrm{0}} ^{+\infty} {F}\left({x}\right){dx} \\ $$ Commented by mathmax by abdo…
Question Number 79104 by mathmax by abdo last updated on 22/Jan/20 $${decompose}\:{F}\left({x}\right)=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}^{\mathrm{2}} −\mathrm{2}^{\mathrm{2}} \right)….\left({x}^{\mathrm{2}} −{n}^{\mathrm{2}} \right)}\:{inside}\:{R}\left({x}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 79102 by mathmax by abdo last updated on 22/Jan/20 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{{ln}\left(\mathrm{1}+{e}^{−{x}^{\mathrm{2}} } \right)−{ln}\left(\mathrm{2}\right)}{{x}^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last updated…