Question Number 98309 by Rio Michael last updated on 12/Jun/20 $$\mathrm{let}\:{f}\left({x}\right)\:=\:\mathrm{ln}\left(\:\mathrm{1}\:+\:\mathrm{cosh}\:\mathrm{2}{x}\right) \\ $$$$\mathrm{show}\:\mathrm{that}\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{f}\left({x}\right)\:=\:\mathrm{2}{x}\:−\:\mathrm{ln}\:\mathrm{2} \\ $$$$\mathrm{hence}\:\mathrm{deduce}\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:{f}\left({x}\right)\:\mathrm{with}\:\mathrm{the}\:\mathrm{asympotes}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{curve}. \\ $$ Answered by abdomathmax last…
Question Number 98286 by M±th+et+s last updated on 12/Jun/20 $${justify}: \\ $$$$\underset{{x}\rightarrow+\infty} {{lim}}\:\underset{{k}\geqslant\mathrm{1}} {\sum}\frac{\left({k}−\mathrm{1}\right)!\:{sin}\left({x}−\frac{\pi}{\mathrm{2}}{k}\right)}{{x}^{{k}} }=\frac{\pi}{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32755 by 7991 last updated on 01/Apr/18 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:=\:….??? \\ $$ Commented by Rio Mike last updated on 01/Apr/18 $$\mathrm{solution} \\…
Question Number 163692 by mathlove last updated on 09/Jan/22 $$ \\ $$A 10 liter bottle filled with a 20% alcohol solution. How much 75% alcohol…
Question Number 163687 by gbanda95 last updated on 09/Jan/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 98148 by M±th+et+s last updated on 11/Jun/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 98135 by Tony Lin last updated on 11/Jun/20 $${how}\:{to}\:{split}\:{x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} \:{into} \\ $$$$\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\left({x}+{y}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\left({x}−{y}\right)^{\mathrm{2}} \:? \\ $$ Commented by MJS last updated on…
Question Number 98116 by M±th+et+s last updated on 11/Jun/20 $${prove}\:{the}\:{compact}\:{form}\:{of}\:{multivariable} \\ $$$${Taylor}\:{series} \\ $$$$ \\ $$$$\left({T}\ast{B}\right)=\underset{{n}=\mathrm{1},{n}=\mathrm{2}..{n}_{{d}} =\mathrm{0}} {\overset{\infty} {\sum}}\frac{\prod_{\mathrm{i}=\mathrm{0}} ^{{n}_{{d}} } \left({x}_{\mathrm{i}} −{d}_{\mathrm{i}} \right)}{\prod_{\mathrm{i}=\mathrm{0}} ^{{n}_{{d}}…
Question Number 98112 by M±th+et+s last updated on 11/Jun/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{2}^{{n}^{\mathrm{2}} } } \\ $$ Answered by maths mind last updated on 11/Jun/20 $${lets}\:{use}…
Question Number 98060 by M±th+et+s last updated on 11/Jun/20 $${show}\:{that} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{arctan}\left(\frac{\mathrm{2}}{{n}^{\mathrm{2}} }\right)=\frac{\mathrm{3}\pi}{\mathrm{4}} \\ $$ Answered by smridha last updated on 11/Jun/20 $${is}\:{it}\:\boldsymbol{{right}}\:\boldsymbol{{ans}}???\boldsymbol{{I}}\:{think}\:\boldsymbol{{it}}'{s}\:{just}…