Question Number 70742 by Joel122 last updated on 07/Oct/19 $$\mathrm{Prove}\:\mathrm{that}\:{f}\left({x}\right)\:=\:{x}\:−\:{a}\:\mathrm{cos}\:\left({x}\right)\:−\:{b} \\ $$$$\mathrm{has}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{real}\:\mathrm{root}\:\mathrm{for}\:\forall{a},{b}\:\in\:\mathbb{R} \\ $$ Commented by kaivan.ahmadi last updated on 07/Oct/19 $${x}−{acosx}−{b}=\mathrm{0}\Rightarrow{x}−{b}={acosx} \\ $$$${y}_{\mathrm{1}} ={x}−{b}…
Question Number 5207 by FilupSmith last updated on 30/Apr/16 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{{S}−\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{i}!\right)}{{n}}−\mathrm{1}={L} \\ $$$${S}\in\mathbb{R},\:\:{S}>\mathrm{0} \\ $$$$ \\ $$$$\mathrm{What}\:\mathrm{can}\:\mathrm{we}\:\mathrm{tell}\:\mathrm{about}\:{L}? \\ $$$$ \\ $$$$\mathrm{Does}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{a}\:\mathrm{limit}? \\ $$$$\mathrm{Is}\:\mathrm{it}\:\mathrm{positive}/\mathrm{negative}?…
Question Number 136279 by aupo14 last updated on 20/Mar/21 Answered by mindispower last updated on 20/Mar/21 $$=\int{e}^{{x}+\frac{\mathrm{1}}{{x}}} {dx}+\int{x}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){e}^{{x}+\frac{\mathrm{1}}{{x}}} {dx}={A} \\ $$$$\mathrm{2}{nd}\:{by}\:{part} \\ $$$$\int{x}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){e}^{{x}+\frac{\mathrm{1}}{{x}}}…
Question Number 5205 by Rojaye Shegz last updated on 30/Apr/16 $$\mathrm{Evaluate}; \\ $$$$\int\:\frac{\left({x}−{x}^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} }{{x}^{\mathrm{4}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136278 by adhigenz last updated on 20/Mar/21 $$\mathrm{How}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}? \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\underset{\mathrm{1}} {\overset{{x}} {\int}}\left[\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}}\:−\:{x}\right]\:{dx}}{{x}^{\mathrm{2}} }\:=\:… \\ $$ Answered by MJS_new last updated on…
Question Number 70741 by aliesam last updated on 07/Oct/19 $${f}\left({x}\right)=\begin{cases}{{x}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\leqslant\mathrm{1}}\\{}\\{\mid{x}−\mathrm{2}\mid\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}>\mathrm{1}}\end{cases} \\ $$$$ \\ $$$${find}\:{the}\:{critical}\:{points} \\ $$ Commented by kaivan.ahmadi last updated on 07/Oct/19 $${f}\left({x}\right)=\begin{cases}{{x}^{\mathrm{2}}…
Question Number 70738 by ajfour last updated on 07/Oct/19 Commented by ajfour last updated on 07/Oct/19 $${Find}\:\:\frac{{R}}{{a}}\:\centerdot \\ $$ Commented by ajfour last updated on…
Question Number 5203 by FilupSmith last updated on 30/Apr/16 $$\mathrm{Silly}\:\mathrm{question} \\ $$$$ \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\frac{{a}}{{b}}}}×\frac{\mathrm{1}}{{b}} \\ $$$$ \\ $$$$\mathrm{Does}\:\mathrm{this}\:\mathrm{equal}: \\ $$$$\frac{\mathrm{1}}{{b}\sqrt{\frac{{a}}{{b}}}}=\frac{\mathrm{1}}{\:\sqrt{{b}^{\mathrm{2}} \frac{{a}}{{b}}}}=\frac{\mathrm{1}}{\:\sqrt{{ab}}}\:???? \\ $$$$ \\ $$$$\mathrm{Ive}\:\mathrm{never}\:\mathrm{done}\:\mathrm{this}\:\mathrm{so}\:\mathrm{it}\:\mathrm{has}\:\mathrm{oddly}\:\mathrm{surprised}\:\mathrm{me}…
Question Number 136268 by EDWIN88 last updated on 20/Mar/21 $$\mathrm{Solve}\:\mathrm{sin}\:\left(\mathrm{2x}\right)−\mathrm{2sin}\:^{\mathrm{2}} \left(\mathrm{x}\right)=\sqrt{\mathrm{3}}\:\mathrm{cos}\:\mathrm{x}\:\mathrm{for}\: \\ $$$$\mathrm{x}\:\mathrm{real}\:\mathrm{and}\:\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{2}\pi \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 5198 by sanusihammed last updated on 29/Apr/16 $${If}\:{the}\:{length}\:{of}\:{a}\:{rope}\:{that}\:{is}\:{attatched}\:{to}\:{a}\:{wall}\:{with}\:{the}\:{period} \\ $$$${of}\:\mathrm{2}{s}\:{is}\:{doubled}\:{what}\:{is}\:{the}\:{new}\:{period}. \\ $$ Commented by prakash jain last updated on 29/Apr/16 $$\mathrm{T}=\mathrm{2}\pi\sqrt{\frac{{l}}{{g}}} \\ $$$$\mathrm{If}\:{l}\:\mathrm{is}\:\mathrm{small}\:\mathrm{compared}\:\mathrm{to}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{Earth}…