Question Number 68346 by peter frank last updated on 09/Sep/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 2791 by Filup last updated on 27/Nov/15 $$\mathrm{Knowing}\:\mathrm{that}\:{e}=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{i}!}, \\ $$$$\mathrm{Show}\:\mathrm{that}\:{e}\:\mathrm{is}\:\mathrm{finite}. \\ $$$$ \\ $$$$\mathrm{That}\:\mathrm{is},\:\mathrm{show}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{true}: \\ $$$${S}=\left\{\exists{x}\in\mathbb{R}:\mid{x}\mid<\infty,\:{e}={x}\right\} \\ $$$$\mathrm{Where}\:{S}\:\mathrm{is}\:\mathrm{the}\:\mathrm{solution} \\ $$ Commented…
Question Number 2777 by Filup last updated on 27/Nov/15 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\zeta\left(−\mathrm{2}{n}\right)=\mathrm{0} \\ $$ Answered by prakash jain last updated on 27/Nov/15 $$\mathrm{Functional}\:\mathrm{Equation}\:\mathrm{for}\:\zeta\left({s}\right) \\ $$$$\zeta\left({s}\right)=\mathrm{2}^{{s}}…
Question Number 68294 by peter frank last updated on 08/Sep/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 68272 by peter frank last updated on 08/Sep/19 Answered by Kunal12588 last updated on 08/Sep/19 $${H}_{{max}} ={maximum}\:{height} \\ $$$${R}={horizontal}\:{range} \\ $$$${H}_{{max}} ={h}=\frac{{u}_{{y}} ^{\mathrm{2}}…
Question Number 2702 by Filup last updated on 25/Nov/15 $$\zeta\left({s}\right)=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}{i}^{−{s}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{{s}} }+\frac{\mathrm{1}}{\mathrm{3}^{{s}} }+… \\ $$$$ \\ $$$$\mathrm{Is}\:\zeta\left({s}\right)>\mathrm{0}\forall{s}\in\mathbb{R}? \\ $$$$\mathrm{1}.\:\mathrm{Can}\:\mathrm{you}\:\mathrm{prove},\:\mathrm{or}\:\mathrm{prove}\:\mathrm{otherwise}? \\ $$$$\mathrm{2}.\:\mathrm{If}\:\zeta\left({s}\right)>{n},\:{s}\in\mathbb{R},\:\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{bounds} \\ $$$$\mathrm{of}\:{s}?\:\mathrm{i}.\mathrm{e}.\:\:{a}\leqslant{s}\leqslant{b}\::\:\zeta\left({s}\right)>{n}…
Question Number 133764 by liberty last updated on 24/Feb/21 Answered by EDWIN88 last updated on 24/Feb/21 $$\:\mathrm{let}\:\mathrm{x}\:\mathrm{be}\:\mathrm{a}\:\mathrm{page}\:\mathrm{number}\:\mathrm{was}\:\mathrm{counted}\:\mathrm{twice} \\ $$$$\mathrm{Assuming}\:\mathrm{the}\:\mathrm{pages}\:\mathrm{start}\:\mathrm{counting}\:\mathrm{at}\:\mathrm{1}\:\mathrm{and} \\ $$$$\mathrm{count}\:\mathrm{continously}\:\mathrm{up}\:\mathrm{we}\:\mathrm{use}\:\mathrm{formula} \\ $$$$\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+…+\mathrm{n}\right)+\mathrm{x}\:=\:\mathrm{1999}\: \\ $$$$\Rightarrow\mathrm{x}\:+\frac{\mathrm{n}\left(\mathrm{n}+\mathrm{1}\right)}{\mathrm{2}}\:=\:\mathrm{1999}\:;\:\mathrm{since}\:\mathrm{x}\:\mathrm{is}\:\mathrm{positive}\:…
Question Number 68212 by peter frank last updated on 07/Sep/19 Answered by $@ty@m123 last updated on 07/Sep/19 $${Let}\:{required}\:{equation}\:{of}\:{line}: \\ $$$${y}={m}_{\mathrm{1}} {x}+{c}\:\:\:…..\left(\mathrm{1}\right) \\ $$$${Given}\:{line}:\:\mathrm{4}{x}+\mathrm{3}{y}=\mathrm{21} \\ $$$${Its}\:{slope}:\:{m}_{\mathrm{2}}…
Question Number 68210 by peter frank last updated on 07/Sep/19 Answered by $@ty@m123 last updated on 08/Sep/19 $${Let}\:\frac{\mathrm{sin}\:{A}}{{a}}=\frac{\mathrm{sin}\:{B}}{{b}}=\frac{\mathrm{sin}\:{C}}{{c}}={R} \\ $$$$\Rightarrow\mathrm{sin}\:{A}={aR},\:\mathrm{sin}\:{B}={bR},\:\mathrm{sin}\:{C}={cR}\:…\left(\mathrm{1}\right) \\ $$$$\left(\mathrm{2}\right)\:\frac{\mathrm{sin}\:\left({A}−{B}\right)\mathrm{sin}\:{C}}{\mathrm{1}+\mathrm{cos}\:\left({A}−{B}\right)\mathrm{cos}\:{C}} \\ $$$$=\:\frac{\mathrm{sin}\:\left({A}−{B}\right)\mathrm{sin}\:\left({A}+{B}\right)}{\mathrm{1}−\mathrm{cos}\:\left({A}−{B}\right)\mathrm{cos}\:\left({A}+{B}\right)} \\…
Question Number 68209 by peter frank last updated on 07/Sep/19 Terms of Service Privacy Policy Contact: info@tinkutara.com