Menu Close

Author: Tinku Tara

Question-69597

Question Number 69597 by ozodbek last updated on 25/Sep/19 Commented by mathmax by abdo last updated on 25/Sep/19 $${generally}\:{let}\:{find}\:{f}\left({a}\right)\:=\int\sqrt{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$${changement}\:{x}\:={ash}\left({t}\right)\:{give}\:{f}\left({a}\right)=\int{ach}\left({t}\right){ach}\left({t}\right){dt} \\ $$$$={a}^{\mathrm{2}}…

Question-69594

Question Number 69594 by ahmadshahhimat775@gmail.com last updated on 25/Sep/19 Answered by MJS last updated on 25/Sep/19 $$\mathrm{2}\leqslant{n}\leqslant\mathrm{4}:\:\mathrm{2}^{{n}!} <\mathrm{2}^{{n}} ! \\ $$$$\mathrm{5}\leqslant{n}:\:\mathrm{2}^{{n}!} >\mathrm{2}^{{n}} ! \\ $$$$\mathrm{ln}\:\mathrm{2}^{{n}!}…

Question-69593

Question Number 69593 by ahmadshahhimat775@gmail.com last updated on 25/Sep/19 Commented by mathmax by abdo last updated on 25/Sep/19 $${let}\:{f}\left({x}\right)\:=\frac{\sqrt{\mathrm{6}−{x}}−\mathrm{2}}{\mathrm{3}−\sqrt{\mathrm{11}−{x}}}\:\Rightarrow \\ $$$${lim}_{{x}\rightarrow\mathrm{2}} \:{f}\left({x}\right)\:={lim}_{{x}\rightarrow\mathrm{2}} \:\:\:\:\:\frac{\left(\sqrt{\mathrm{6}−{x}}−\mathrm{2}\right)\left(\sqrt{\mathrm{6}−{x}}+\mathrm{2}\right)\left(\mathrm{3}+\sqrt{\mathrm{11}−{x}}\right)}{\left(\mathrm{3}−\sqrt{\mathrm{11}−{x}}\right)\left(\mathrm{3}+\sqrt{\mathrm{11}−{x}}\right)\left(\sqrt{\mathrm{6}−{x}}+\mathrm{2}\right)} \\ $$$$={lim}_{{x}\rightarrow\mathrm{2}}…