Question Number 69786 by mathmax by abdo last updated on 27/Sep/19 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last…
Question Number 4250 by Yozzii last updated on 06/Jan/16 $${Let}\:{u}=\frac{{ln}\left(\mathrm{3}−\left\{\frac{{ln}\left(\mathrm{3}−\left[\frac{{ln}\left(\mathrm{3}−\left(\ldots\right.\right.}{{ln}\left(\mathrm{2}+\left(\ldots\right.\right.}\right.\right.}{{ln}\left(\mathrm{2}+\left[\frac{{ln}\left(\mathrm{3}−\left(\ldots\right.\right.}{{ln}\left(\mathrm{2}+\left(\ldots\right.\right.}\right.\right.}\right\}\right)}{{ln}\left(\mathrm{2}+\left\{\frac{{ln}\left(\mathrm{3}−\left[\frac{{ln}\left(\mathrm{3}−\left(\ldots\right.\right.}{{ln}\left(\mathrm{2}+\left(\ldots\right.\right.}\right.\right.}{{ln}\left(\mathrm{2}+\left[\frac{{ln}\left(\mathrm{3}−\left(\ldots\right.\right.}{{ln}\left(\mathrm{2}+\left(\ldots\right.\right.}\right.\right.}\right\}\right)}. \\ $$$${What}\:{is}\:{the}\:{value}\:{of}\:{u}?\: \\ $$$$ \\ $$$${Let}\:{k}=\frac{{ln}\left({x}−\left\{\frac{{ln}\left({x}−\left[\frac{{ln}\left({x}−\left(\ldots\right.\right.}{{ln}\left({x}−\mathrm{1}+\left(\ldots\right.\right.}\right.\right.}{{ln}\left({x}−\mathrm{1}+\left[\frac{{ln}\left({x}−\left(\ldots\right.\right.}{{ln}\left({x}−\mathrm{1}+\left(\ldots\right.\right.}\right.\right.}\right\}\right)}{{ln}\left({x}−\mathrm{1}+\left\{\frac{{ln}\left({x}−\left[\frac{{ln}\left({x}−\left(\ldots\right.\right.}{{ln}\left({x}−\mathrm{1}+\left(\ldots\right.\right.}\right.\right.}{{ln}\left({x}−\mathrm{1}+\left[\frac{{ln}\left({x}−\left(\ldots\right.\right.}{{ln}\left({x}−\mathrm{1}+\left(\ldots\right.\right.}\right.\right.}\right\}\right)}. \\ $$$${For}\:{what}\:{values}\:{of}\:{x}\:{does} \\ $$$$\left({i}\right)\:{k}\:{converge}\:\left({ii}\right)\:{k}\:{diverge}? \\ $$ Commented by Yozzii…
Question Number 69784 by mathmax by abdo last updated on 27/Sep/19 $${calculate}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left({x}^{\mathrm{2}} \:+\frac{{a}}{{x}^{\mathrm{2}} }\right)} {dx}\:\:{with}\:{a}>\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 135313 by bobhans last updated on 12/Mar/21 $${Given}\:{f}\left({x}\right)\:=\:\mathrm{5}{x}+\mathrm{cos}\:\left(\mathrm{3}{x}\right) \\ $$$${Find}\:{the}\:{value}\:{of}\:\frac{{d}}{{dx}}\:\left[{f}^{−\mathrm{1}} \left(\mathrm{1}\right)\right] \\ $$ Answered by liberty last updated on 12/Mar/21 $$\left(\mathrm{1}\right){f}\left(\mathrm{0}\right)=\mathrm{1}\Leftrightarrow{f}^{−\mathrm{1}} \left(\mathrm{1}\right)=\mathrm{0} \\…
Question Number 69778 by Rio Michael last updated on 27/Sep/19 $${prove}\:{that}\:{the}\:{equation}\: \\ $$$$\:\:\left({b}^{\mathrm{2}} −\mathrm{4}{ac}\right){x}^{\mathrm{2}} \:+\:\mathrm{4}\left({a}\:+\:{c}\right){x}\:−\mathrm{4}\:=\:\mathrm{0}\:{is}\:{always}\:{real}. \\ $$ Commented by prakash jain last updated on 28/Sep/19…
Question Number 4242 by prakash jain last updated on 05/Jan/16 $$\mathrm{Find}\:\mathrm{that}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{2}^{\mathrm{2}^{\mathrm{2}\centerdot\centerdot\centerdot} } \:\:\left(\mathrm{continued}\:\mathrm{power}\:\mathrm{of}\:\mathrm{2}\right) \\ $$$$\mathrm{using}\:\mathrm{analytical}\:\mathrm{continuation}. \\ $$ Commented by RasheedSindhi last updated on…
Question Number 135309 by mnjuly1970 last updated on 12/Mar/21 $$\:\:\:\:\:\:\:\:\:\:….\:\:\mathscr{N}{ice}\:\:\:\:\mathscr{C}{alculus}\:…. \\ $$$$\:\:\:\:\:\:\:\:{prove}\:\:{that}\:::: \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({ksin}\alpha\right){x}}{\:\sqrt{{x}}}{dx}=\sqrt{\frac{\pi}{{k}}}\:{sin}\left(\frac{\alpha}{\mathrm{2}}\right)… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\: \\ $$ Answered by mathmax…
Question Number 135308 by bobhans last updated on 12/Mar/21 Commented by mr W last updated on 12/Mar/21 $${at}\:{t}=\mathrm{3}\:{s},\:{the}\:{height}\:{is}\:\mathrm{71}.\mathrm{65}{m} \\ $$$${at}\:{t}=\mathrm{7}.\mathrm{8009}{s},\:{the}\:{ball}\:{hits}\:{the}\:{ground} \\ $$$${max}.\:{height}\:{is}\:\mathrm{75}.\mathrm{4235}{m} \\ $$$${in}\:\mathrm{6}.\mathrm{1554}−\mathrm{1}.\mathrm{5997}=\mathrm{4}.\mathrm{5557}{s}\:{the}\:{ball} \\…
Question Number 135305 by JulioCesar last updated on 12/Mar/21 Answered by MJS_new last updated on 12/Mar/21 $$\int\frac{{dx}}{{a}^{{x}} +{b}}= \\ $$$$\:\:\:\:\:\left[{t}={a}^{{x}} +{b}\:\rightarrow\:{dx}=\frac{{dt}}{{a}^{{x}} \mathrm{ln}\:{a}}\right] \\ $$$$=\frac{\mathrm{1}}{\mathrm{ln}\:{a}}\int\frac{{dt}}{{t}\left({t}−{b}\right)}=\frac{\mathrm{1}}{{b}\mathrm{ln}\:{a}}\int\left(\frac{\mathrm{1}}{{t}−{b}}−\frac{\mathrm{1}}{{t}}\right){dt}= \\…
Question Number 4234 by Filup last updated on 04/Jan/16 $${n},\:{m}\in\mathbb{Z} \\ $$$${n}!={n}\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right)… \\ $$$$ \\ $$$$\mathrm{if}\:{n}!={m}\:\mathrm{where}\:\mathrm{we}\:\mathrm{know}\:\mathrm{the}\:\mathrm{value} \\ $$$${m}\:\mathrm{but}\:\mathrm{not}\:{n},\:\mathrm{can}\:\mathrm{we}\:\mathrm{solve}\:\mathrm{for}\:{n}? \\ $$ Commented by prakash jain last…