Question Number 134812 by mohammad17 last updated on 07/Mar/21 $$\int\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+{cosh}\left({t}\right)\right.}\:\:{dt} \\ $$ Answered by mathmax by abdo last updated on 07/Mar/21 $$\mathrm{I}=\int\sqrt{\frac{\mathrm{1}+\mathrm{ch}\left(\mathrm{t}\right)}{\mathrm{2}}}\mathrm{dt}\:=\int\sqrt{\mathrm{ch}^{\mathrm{2}} \left(\frac{\mathrm{t}}{\mathrm{2}}\right)}\mathrm{dt}\:=\int\:\mathrm{ch}\left(\frac{\mathrm{t}}{\mathrm{2}}\right)\mathrm{dt} \\ $$$$=\mathrm{2sh}\left(\frac{\mathrm{t}}{\mathrm{2}}\right)\:+\mathrm{C}…
Question Number 69276 by mr W last updated on 22/Sep/19 $${f}\left({x}\right)=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\mid{x}+{k}\mid \\ $$$$\left(\mathrm{1}\right)\:{find}\:{the}\:{values}\:{of}\:{x}\:{such}\:{that}\:{f}\left({x}\right)\: \\ $$$${is}\:{minumum}. \\ $$$$\left(\mathrm{2}\right)\:{fund}\:{the}\:{roots}\:{of}\:{f}\left({x}\right)−{m}=\mathrm{0} \\ $$$$ \\ $$$${as}\:{example}\:{you}\:{can}\:{set}\:{n}=\mathrm{100},\:{m}=\mathrm{2500}. \\ $$…
Question Number 134814 by Ndala last updated on 07/Mar/21 Commented by Ndala last updated on 07/Mar/21 $$\mathrm{I}\:\mathrm{need}\:\mathrm{your}\:\mathrm{help}\:\mathrm{my}\:\mathrm{friends}! \\ $$ Answered by Ar Brandon last updated…
Question Number 134809 by liberty last updated on 07/Mar/21 $${Show}\:{if}\:{f}\:''\left({a}\right)\:{exist}\:{then}\: \\ $$$${f}\:''\left({a}\right)=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{f}\left({a}+{h}\right)+{f}\left({a}−{h}\right)−\mathrm{2}{f}\left({a}\right)}{{h}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 134811 by bramlexs22 last updated on 07/Mar/21 $$\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \:\frac{\mathrm{sin}\:\left(\frac{\mathrm{3x}}{\mathrm{2}}\right)}{\mathrm{tan}\:\left(\mathrm{3x}\right)}\:\mathrm{dx} \\ $$ Answered by EDWIN88 last updated on 07/Mar/21 $$\mathrm{set}\:\frac{\mathrm{3x}}{\mathrm{2}}\:=\:\mathrm{t}\:\Rightarrow\:\mathrm{3x}\:=\:\mathrm{2t}\:,\:\begin{array}{|c|c|}{\mathrm{x}=\frac{\pi}{\mathrm{2}}\rightarrow\mathrm{t}=\frac{\mathrm{3}\pi}{\mathrm{4}}}\\{\mathrm{x}=\mathrm{0}\:\rightarrow\mathrm{t}=\mathrm{0}}\\\hline\end{array} \\ $$$$\mathbb{L}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{3}\pi/\mathrm{4}}…
Question Number 69272 by TawaTawa last updated on 22/Sep/19 Answered by $@ty@m123 last updated on 22/Sep/19 $${Let}\:\angle{DPC}=\theta \\ $$$$\Rightarrow\angle{Q}=\theta−\mathrm{30} \\ $$$${Let}\:{CP}={x} \\ $$$${In}\:\bigtriangleup{DCP}, \\ $$$$\mathrm{tan}\:\theta=\frac{\sqrt{\mathrm{3}}}{{x}}\:…\left(\mathrm{1}\right)…
Question Number 3735 by prakash jain last updated on 19/Dec/15 $$\mathrm{Prove} \\ $$$$\underset{{m}=\mathrm{0}} {\overset{\infty} {\sum}}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{{mn}}{\mathrm{2}^{{m}+{n}} }=\mathrm{4} \\ $$ Commented by prakash jain last…
Question Number 3734 by prakash jain last updated on 19/Dec/15 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{{n}}{\mathrm{2}^{{n}} }=? \\ $$ Answered by prakash jain last updated on 19/Dec/15 $${a}_{{n}}…
Question Number 69268 by A8;15: last updated on 22/Sep/19 Answered by mr W last updated on 22/Sep/19 $${x}^{{x}^{\mathrm{20}} } =\mathrm{2}^{\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}} \\ $$$${x}^{{x}} =\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{20}\sqrt{\mathrm{2}}}} ={a} \\…
Question Number 134801 by faysal last updated on 07/Mar/21 Answered by EDWIN88 last updated on 07/Mar/21 $$\mathrm{13}\theta\:=\:\pi\:\Rightarrow\mathrm{cos}\:\mathrm{13}\theta\:=\:−\mathrm{1} \\ $$$$\mathrm{let}\::\:\mathrm{z}\:=\:\mathrm{cos}\:\theta\:\mathrm{cos}\:\mathrm{2}\theta\:\mathrm{cos}\:\mathrm{3}\theta\:\mathrm{cos}\:\mathrm{4}\theta\:\mathrm{cos}\:\mathrm{5}\theta\:\mathrm{cos}\:\mathrm{6}\theta \\ $$$$\mathrm{2z}\:\mathrm{sin}\:\theta\:=\:\mathrm{sin}\:\mathrm{2}\theta\:\mathrm{cos}\:\mathrm{2}\theta\:\mathrm{cos}\:\mathrm{3}\theta\:\mathrm{cos}\:\mathrm{4}\theta\:\mathrm{cos}\:\mathrm{5}\theta\:\mathrm{cos}\:\mathrm{6}\theta \\ $$$$\mathrm{4z}\:\mathrm{sin}\:\theta\:=\:\mathrm{sin}\:\mathrm{4}\theta\:\mathrm{cos}\:\mathrm{3}\theta\:\mathrm{cos}\:\mathrm{4}\theta\:\mathrm{cos}\:\mathrm{5}\theta\:\mathrm{cos}\:\mathrm{6}\theta \\ $$$$\mathrm{8z}\:\mathrm{sin}\:\theta\:=\:\mathrm{sin}\:\mathrm{8}\theta\:\mathrm{cos}\:\mathrm{3}\theta\:\mathrm{cos}\:\mathrm{5}\theta\:\mathrm{cos}\:\mathrm{6}\theta…