Question Number 126732 by 0731619177 last updated on 23/Dec/20 Answered by Dwaipayan Shikari last updated on 24/Dec/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left[\psi\left({x}\right)+\frac{\mathrm{1}}{{x}}\right]=−\gamma+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}}−\frac{\mathrm{1}}{\left({n}−\mathrm{1}\right)+{x}}+\frac{\mathrm{1}}{{x}} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}}−\frac{\mathrm{1}}{\left({n}−\mathrm{1}\right)+{x}}\sim−\frac{\mathrm{1}}{{x}}\:\:\left({x}\:{is}\:{very}\:{small}\:{with}\:{respect}\:{to}\:\overset{\infty}…
Question Number 192270 by universe last updated on 13/May/23 $$\:{prove}\:{that} \\ $$$$\:\:\mathrm{sin}\:\mathrm{50}°\:+\:\mathrm{sin}\:\mathrm{10}°\:=\:\mathrm{cos}\:\mathrm{20}° \\ $$ Answered by Frix last updated on 13/May/23 $$\mathrm{sin}\:\left(\mathrm{60}°−\mathrm{10}°\right)\:+\mathrm{sin}\:\mathrm{10}°= \\ $$$$=\mathrm{sin}\:\mathrm{60}°\:\mathrm{cos}\:\mathrm{10}°\:−\mathrm{cos60}°\:\mathrm{sin}\:\mathrm{10}°\:+\mathrm{sin}\:\mathrm{10}°\:= \\…
Question Number 192265 by yaslm last updated on 13/May/23 Answered by Frix last updated on 13/May/23 $${x}={p}+\mathrm{1} \\ $$$${y}={q}+\mathrm{1} \\ $$$$\left({p},\:{q}\right)\:\rightarrow\:\left(\mathrm{0},\:\mathrm{0}\right) \\ $$$$\frac{\left({x}−{y}\right)^{\mathrm{2}} }{{x}−{y}^{\mathrm{2}} }=−\frac{\left({p}−{q}\right)^{\mathrm{2}}…
Question Number 126731 by 0731619177 last updated on 23/Dec/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 192266 by Shlock last updated on 13/May/23 Answered by Frix last updated on 13/May/23 $$\mathrm{Since}\:{a}\in\mathbb{N}\wedge\mathrm{0}\leqslant{a}\leqslant\mathrm{9}\:\mathrm{it}'\mathrm{s}\:\mathrm{best}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{for} \\ $$$${n}\:\mathrm{and}\:\mathrm{try}: \\ $$$$\mathrm{2}{n}^{\mathrm{2}} +\mathrm{14}{n}+\mathrm{83}=\mathrm{1111}{a} \\ $$$${n}=\frac{−\mathrm{7}+\sqrt{\mathrm{2222}{a}−\mathrm{117}}}{\mathrm{2}} \\…
Question Number 192261 by mnjuly1970 last updated on 13/May/23 $$ \\ $$$$\:\:\:{f}\left({x}\right)=\lfloor\:\frac{\:\mathrm{1}}{\mathrm{1}+\sqrt{{x}}}\:\rfloor\:{is}\:{derivable}\: \\ $$$$\:\:{on}\:\:\left(\:\mathrm{0}\:,\:\:{k}\:\right).\:{find}\:{the}\:{value}\:{of} \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{k}_{\:{max}} =?\: \\ $$$$\:\:\: \\ $$ Terms of…
Question Number 126726 by mnjuly1970 last updated on 23/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:{calculus}… \\ $$$$\:\:{prove}\:\:{that}\::\: \\ $$$$\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}\:} {\overset{\infty} {\sum}}\frac{\mathrm{H}_{{n}} }{{n}^{\mathrm{4}} }\:\overset{?} {=}\mathrm{3}\zeta\left(\mathrm{5}\right)−\zeta\left(\mathrm{2}\right)\left(\mathrm{3}\right)\:\:…. \\ $$$$\:\:\:{where}::\:\:\:\:\mathrm{H}_{{n}\:} \:=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}\:+…+\frac{\mathrm{1}}{{n}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………. \\…
Question Number 192257 by Tomal last updated on 13/May/23 $$ \\ $$$$\mathrm{A}\:\mathrm{bullet}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{30}\:\mathrm{ms}^{−\mathrm{1}} \:\mathrm{after} \\ $$$$\mathrm{pentrating}\:\mathrm{a}\:\mathrm{6}\:{cm}\:\mathrm{whole}\:\mathrm{tree}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{is}\: \\ $$$$\mathrm{reduced}\:\mathrm{by}\:\mathrm{one}−\mathrm{third}\:\mathrm{and}\:\mathrm{then}\:\mathrm{the}\:\mathrm{bullet} \\ $$$$\mathrm{travel}{s}\:\mathrm{for}\:\mathrm{1s}\:\mathrm{more}.\: \\ $$$$ \\ $$$$ \\ $$$${Will}\:\mathrm{the}\:\mathrm{bullet}\:\mathrm{penetratee}…
Question Number 126722 by 0731619177 last updated on 23/Dec/20 Answered by mahdipoor last updated on 23/Dec/20 $${x}=\mathrm{5\begin{cases}{{x}!!!−\mathrm{10}>\mathrm{0}}\\{\mathrm{2}{x}−\mathrm{10}=\mathrm{0}}\end{cases}} \\ $$$${l}\underset{{x}\rightarrow\mathrm{5}^{−} } {{i}m}\:\frac{{x}!!!−\mathrm{10}}{\mathrm{2}{x}−\mathrm{10}}=−\infty \\ $$$${l}\underset{{x}\rightarrow\mathrm{5}^{+} } {{i}m}\:\frac{{x}!!!−\mathrm{10}}{\mathrm{2}{x}−\mathrm{10}}=+\infty…
Question Number 192256 by Red1ight last updated on 13/May/23 $$\mathrm{given}\:{f}\left({x}\right)={cx}\left({x}−\mathrm{20}\right)\:\mathrm{and}\:{A}=\left(\mathrm{2},\mathrm{5}\right) \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{nearst}\:\mathrm{point}\:\mathrm{to}\:{A}\:\mathrm{on}\:\mathrm{the}\:\mathrm{graph} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com