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Question-76143

Question Number 76143 by Master last updated on 24/Dec/19 Commented by mathmax by abdo last updated on 24/Dec/19 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{4}+{x}^{\mathrm{2}} }{dx}\:\:{changement}\:{x}=\mathrm{2}{sh}\left({t}\right)\:{give} \\ $$$${I}\:=\int_{\mathrm{0}} ^{{argsh}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)}…

Question-141669

Question Number 141669 by bramlexs22 last updated on 22/May/21 Answered by iloveisrael last updated on 22/May/21 $$\left({i}\right)\:{f}\left({a}\right)={g}\left({a}\right)\:,{a}>\mathrm{0} \\ $$$$\Rightarrow\:{a}+\mid\mathrm{2}{a}\mid\:=\:−{a}^{\mathrm{2}} −\frac{\mathrm{2}}{\mathrm{3}}{a}+\frac{\mathrm{14}}{\mathrm{3}} \\ $$$$\Rightarrow\mathrm{3}{a}\:=−{a}^{\mathrm{2}} −\frac{\mathrm{2}}{\mathrm{3}}{a}+\frac{\mathrm{14}}{\mathrm{3}} \\ $$$$\Rightarrow\mathrm{3}{a}^{\mathrm{2}}…

Advanced-Calculus-if-n-2-1-n-n-2-n-then-prove-that-1-2-e-1-proof-method-1-

Question Number 141668 by mnjuly1970 last updated on 22/May/21 $$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:…….{Advanced}\:…\bigstar\:…\bigstar\:…\:{Calculus}……. \\ $$$$\:\:\:\:\:\:\:\:\:{if}\:\:\:\:\Omega\:=\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} \zeta\left({n}\right)}{\mathrm{2}^{{n}} }\:{then}\:{prove} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{that}\:::\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:=\:{e}^{\Omega−\mathrm{1}} \:\: \\ $$$$\:\:\:\:{proof}\::: \\ $$$$\:\:\:\:{method}\:\left(\mathrm{1}\right):…

Question-76126

Question Number 76126 by Master last updated on 24/Dec/19 Commented by benjo last updated on 24/Dec/19 Commented by benjo last updated on 24/Dec/19 $$\mathrm{i}\:\mathrm{cannot}\:\mathrm{find}\:\mathrm{formula}\:\mathrm{the}\:\mathrm{simple}\:\mathrm{form}\:\mathrm{n}−\:\mathrm{th} \\…

x-2-x-12-x-15-k-x-16-find-x-in-terms-of-k-gt-0-

Question Number 141663 by ajfour last updated on 22/May/21 $$\:\underset{\:\:−−−−−−−−−−−−−−−−−−−} {\:} \\ $$$$\:\:{x}^{\mathrm{2}} \left({x}−\mathrm{12}\right)\left({x}−\mathrm{15}\right)={k}\left({x}−\mathrm{16}\right) \\ $$$$\:\:\:\:{find}\:{x}\:{in}\:{terms}\:{of}\:{k}\:\left(>\mathrm{0}\right). \\ $$$$\:\:\overset{−−−−−−−−−−−−−−−−−−−} {\:} \\ $$ Commented by Rasheed.Sindhi last…