Question Number 136799 by Dwaipayan Shikari last updated on 26/Mar/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}−{q}^{{n}} \right){dq} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136793 by JulioCesar last updated on 26/Mar/21 Answered by Dwaipayan Shikari last updated on 26/Mar/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{x}^{{sin}\left({ax}\right)} }{{x}^{{tan}\left({bx}\right)} }\right)={y} \\ $$$$\Rightarrow\left({sin}\left({ax}\right)−{tan}\left({bx}\right)\right){log}\left({x}\right)={log}\left({y}\right) \\ $$$$\Rightarrow\left({acos}\left({ax}\right)−{bsec}^{\mathrm{2}}…
Question Number 5723 by Rasheed Soomro last updated on 25/May/16 $$\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{8}}+….+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{n}} }=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{n}} } \\ $$$$\mathrm{P}\:\:\:\mathrm{r}\:\:\:\mathrm{o}\:\:\:\mathrm{v}\:\:\:\mathrm{e}\:\mathrm{the}\:\mathrm{above}\:\mathrm{for}\:\mathrm{integral}\:\mathrm{n}\geqslant\mathrm{1}. \\ $$ Commented by FilupSmith last updated on 25/May/16 $$\boldsymbol{\mathrm{LHS}}={S}=\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{8}}+…+\frac{\mathrm{1}}{\mathrm{2}^{{n}}…
Question Number 136792 by EDWIN88 last updated on 26/Mar/21 $$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{diophantine}\:\mathrm{equation} \\ $$$$\left(\mathrm{1}\right)\mathrm{3xy}\:+\mathrm{2x}\:+\mathrm{y}\:=\:\mathrm{12}\:? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{x}^{\mathrm{3}} =\:\mathrm{4y}^{\mathrm{2}} +\mathrm{4y}−\mathrm{3}\:? \\ $$ Answered by mindispower last updated on 26/Mar/21…
Question Number 5722 by Rasheed Soomro last updated on 25/May/16 $$\mathrm{Prove}\:\mathrm{by}\:\boldsymbol{\mathrm{mathematical}}\:\boldsymbol{\mathrm{induction}} \\ $$$$\mathrm{that}\:\mathrm{tbe}\:\mathrm{following}\:\mathrm{formula}\:\mathrm{is}\:\mathrm{correct} \\ $$$$\mathrm{for}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{n}: \\ $$$$\begin{pmatrix}{\mathrm{2}}\\{\mathrm{2}}\end{pmatrix}\:+\begin{pmatrix}{\mathrm{3}}\\{\mathrm{2}}\end{pmatrix}\:+\begin{pmatrix}{\mathrm{4}}\\{\mathrm{2}}\end{pmatrix}\:+…+\begin{pmatrix}{\mathrm{n}+\mathrm{1}}\\{\:\:\:\mathrm{2}}\end{pmatrix}\:=\begin{pmatrix}{\mathrm{n}+\mathrm{2}}\\{\:\:\:\mathrm{3}}\end{pmatrix} \\ $$ Commented by Yozzii last updated on…
Question Number 71255 by ajfour last updated on 13/Oct/19 Commented by MJS last updated on 13/Oct/19 $$\mathrm{the}\:\mathrm{maximum}\:\mathrm{area}\:\mathrm{depends}\:\mathrm{on}\:{a} \\ $$$$\mathrm{the}\:\mathrm{area}\:\mathrm{for}\:\theta=\mathrm{90}°\:\mathrm{is}\:\frac{\pi}{\mathrm{4}}{b}\:\mathrm{and}\:\mathrm{this}\:\mathrm{value}\:\mathrm{is} \\ $$$$\mathrm{again}\:\mathrm{reached}\:\mathrm{st}\:\theta=\mathrm{45}°.\:\mathrm{this}\:\mathrm{is}\:\mathrm{only}\:\mathrm{possible} \\ $$$$\mathrm{if}\:{a}=\sqrt{\mathrm{2}}{b}\:\mathrm{at}\:\mathrm{least}.\:\mathrm{for}\:{b}\leqslant{a}\leqslant\sqrt{\mathrm{2}}{b}\:\mathrm{the}\:\mathrm{maximum} \\ $$$$\mathrm{area}\:\mathrm{is}\:\frac{\pi}{\mathrm{4}}{b};\:\mathrm{for}\:{a}>\sqrt{\mathrm{2}}{b}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{is}\:\mathrm{at}\:{r}={a}…
Question Number 5718 by Rasheed Soomro last updated on 25/May/16 $$\mathrm{Two}\:\mathrm{angles}\:\mathrm{can}\:\mathrm{be}\:\mathrm{added}\:\mathrm{and}\:\mathrm{subtracted}. \\ $$$$\mathrm{Can}\:\mathrm{we}\:\mathrm{multiply}\:\mathrm{them}\:\mathrm{also}? \\ $$$$\mathrm{For}\:\mathrm{example}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}\:\mathrm{radians}\:×\:\mathrm{y}\:\mathrm{radians}\:=\:\mathrm{xy}\:\left(\mathrm{radians}\right)^{\mathrm{2}} \:? \\ $$$$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{meaning}\:\mathrm{of}\:\:\left(\mathrm{radians}\right)^{\mathrm{2}} \\ $$$$\left(\mathrm{square}\:\mathrm{radians}\right)? \\ $$ Commented…
Question Number 5715 by sanusihammed last updated on 24/May/16 $${Differentiate}\:\:\:{x}^{{x}} \:\:\:{from}\:{the}\:{first}\:{principle}. \\ $$$$ \\ $$$${please}\:{help} \\ $$ Answered by Yozzii last updated on 25/May/16 $${Let}\:{y}={x}^{{x}}…
Question Number 5712 by sanusihammed last updated on 24/May/16 $${Find}\:{the}\:{value}\:{of}\:{x}\: \\ $$$$ \\ $$$$\mathrm{2}^{{x}} \:=\:\mathrm{4}{x} \\ $$$$ \\ $$$${workings}\:{is}\:{needed}\:{please}. \\ $$ Commented by Yozzii last…
Question Number 136781 by bramlexs22 last updated on 25/Mar/21 $$ \\ $$What is the equation of the circle passing though (-2,-4) and (4,6) its center…