Question Number 8244 by lepan last updated on 04/Oct/16 $${Show}\:{that}\:{the}\:{curve}\:{y}={ln}\left(\frac{\mathrm{5}−\mathrm{7}{x}}{\mathrm{8}+{x}}\right)\:{has} \\ $$$${no}\:{stationary}\:{point}\:{for}\:{all}\:{real}\:{values} \\ $$$${of}\:{x}. \\ $$ Answered by 123456 last updated on 06/Oct/16 $${y}=\mathrm{ln}\:\frac{\mathrm{5}−\mathrm{7}{x}}{\mathrm{8}+{x}} \\…
Question Number 73755 by ~blr237~ last updated on 15/Nov/19 $${show}\:{that}\:\:\:{for}\:{all}\:{integer}\:\:{n}\:,\:\:{n}+\mathrm{1}\:{divides}\:\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix} \\ $$ Answered by mind is power last updated on 15/Nov/19 $$\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}=\frac{\left(\mathrm{2}{n}\right)!}{{n}!{n}!}\in\mathbb{N} \\ $$$$\frac{{n}}{{n}+\mathrm{1}}\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}=\frac{\mathrm{2}{n}!}{{n}!.\left({n}\right)!}.\frac{{n}}{{n}+\mathrm{1}}=\frac{\mathrm{2}{n}!}{\left({n}−\mathrm{1}\right)!.\left({n}+\mathrm{1}\right)!}=\begin{pmatrix}{\mathrm{2}{n}}\\{{n}+\mathrm{1}}\end{pmatrix} \\…
Question Number 139276 by mnjuly1970 last updated on 25/Apr/21 Commented by mnjuly1970 last updated on 28/Apr/21 $$\:\:{correct}\:{answer}::\:{e}^{\mathrm{2}} .{e}^{{e}^{\mathrm{2}} } \\ $$ Answered by Dwaipayan Shikari…
Question Number 139255 by bobhans last updated on 25/Apr/21 $$ \\ $$How do you find a point on the curve y = x^2 that is…
Question Number 8113 by uchechukwu okorie favour last updated on 30/Sep/16 $${Find}\:{an}\:{equation}\:{of}\:{the}\:{tangent} \\ $$$${line}\:{to}\:{the}\:{curve}\:{y}={tan}^{\mathrm{2}} {x}\:{at}\:{the}\: \\ $$$${point}\left(\frac{{x}}{\mathrm{3}}\:,\:\mathrm{0}\right) \\ $$ Answered by prakash jain last updated…
Question Number 139171 by mnjuly1970 last updated on 23/Apr/21 Answered by Dwaipayan Shikari last updated on 23/Apr/21 $$\Gamma\left(\mathrm{1}+{x}\right)=\mathrm{1}−\gamma{x}+{O}\left({x}^{\mathrm{2}} \right)\Rightarrow\Gamma\left({x}\right)=\frac{\mathrm{1}}{{x}}−\gamma+{O}\left({x}\right) \\ $$$$\Gamma'\left(\mathrm{1}+{x}\right)=−\gamma+{O}\left({x}\right)\Rightarrow{x}\Gamma\left({x}\right)\psi\left({x}+\mathrm{1}\right)=−\gamma+{O}\left({x}\right) \\ $$$$\Rightarrow{x}\Gamma\left({x}\right)\psi\left({x}\right)+\Gamma\left({x}\right)=−\gamma+{O}\left({x}\right)\Rightarrow\psi\left({x}\right)\sim−\frac{\gamma}{{x}\Gamma\left({x}\right)}−\frac{\mathrm{1}}{{x}} \\ $$$$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 73569 by Rio Michael last updated on 13/Nov/19 $${let}\:{f}\left({x}\right)\:=\:\frac{{tanx}}{{tan}\mathrm{2}{x}}\:.\:{Find}\:{the}\:{points}\:{of}\:{discontinuity} \\ $$$${of}\:{f}\:{on}\:\left[\mathrm{0},\mathrm{2}\pi\right]\:{and}\:{determine}\:{wether}\:{each}\:{duscontinuity}\:{is} \\ $$$${a}\:{point}\:{discontinuity},{a}\:{jump}\:{discontinuity},{or}\:{a}\:{vertical}\:{asymtote} \\ $$$$ \\ $$ Commented by Rio Michael last updated…
Question Number 73560 by mhmd last updated on 13/Nov/19 $${prove}\:{that}\:\left(\mathrm{1}−{itan}\theta\right)/\left({i}+{cot}\theta\right)={itan}\theta \\ $$$${pleas}\:{sir}\:{help}\:{me}? \\ $$ Commented by MJS last updated on 13/Nov/19 $$\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{generally}\:\mathrm{true} \\ $$$$\frac{\mathrm{1}−\mathrm{i}\:\mathrm{tan}\:\theta}{\mathrm{i}+\mathrm{cot}\:\theta}=\mathrm{2sin}\:\theta\:\mathrm{cos}\:\theta\:−\mathrm{tan}\:\theta\:−\mathrm{2i}\:\mathrm{sin}^{\mathrm{2}} \:\theta…
Question Number 7962 by upendrakishor99@gmail.com last updated on 25/Sep/16 $${prove}\:{that}\:\:\:{tanx}<\frac{\mathrm{4}{x}}{\pi}\:{for}\:\mathrm{0}<{x}<\frac{\pi}{\mathrm{4}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 7938 by tawakalitu last updated on 24/Sep/16 $${if}\:\:{f}\left({x}\right)\:=\:{xlog}\left({x}\:+\:{r}\right)\:−\:{r}\:\:{and}\:\:{r}^{\mathrm{2}} \:=\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \\ $$$${prove}\:{that}:\:\:{f}_{{xx}} \:+\:{f}_{{yy}} \:\:=\:\:\frac{\mathrm{1}}{{x}\:+\:{r}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com